**APPARATUS FOR IMPROVED UNDERWATER ACOUSTIC TELEMETRY UTILIZING PHASE COHERENT COMMUNICATIONS**

John

George, Catipovic

Josko, Stojanovic

Milica

*; (IPC1-7): H04B11/00*

**H04B11/00**US5029147A |

1. | Apparatus for digital underwater communication over an underwater acoustic channel comprising: means including a transmitter at a first location for horizontally transmitting a carrier modulated by a phase coherent stream of data corresponding to symbols; means including a receiver at a second location for detecting and demodulating said stream to remove channel induced degradations in said stream, thereby to recover undegradated data in the form of symbols; and means for displaying said recovered symbols, whereby phase coherent communications is established despite an underwater acoustic channel which changes rapidly and ordinarily restricts the data rate. |

2. | The apparatus of claim 1 wherein said detecting and demodulating means includes in combination means for sampling said data stream to produce a sampled signal; means for detecting the intersymbol interval of said sampled signal and for adjusting the sampling rate of said sampling means to correspond in sampling interval to that of the detected intersymbol interval; means for detecting Doppler shift in said carrier and for removing the effects of Doppler shift from said sampled signal to produce a Doppler removed signal; and means including an equalizer coupled to said Doppler removed signal for sensing the differences between a first set of received data symbols and for removing said differences from said sampled signal. |

3. | The apparatus of Claim 2 wherein said intersymbol detecting means includes a feedforward and a feedback equalizer. 57 . |

4. | The apparatus of Claim 3 wherein said equalizers are decision feedback equalizers. |

5. | The apparatus of Claim 2 wherein said equalizers are transversal filters. |

6. | The apparatus of Claim 2 wherein said detecting means includes means coupled to said sampling means for removing said carrier. |

7. | The apparatus of Claim 2 wherein said means for detecting said intersymbol interval includes a feedforward equalizer. |

8. | The apparatus of Claim 2 wherein said means for adjusting said sampling rate includes a timing synchronizer coupled to said detecting means and an interpolator and resampler coupled to said timing synchronizer for varying the interpolator period responsive to the output of said timing synchronizer. |

9. | The apparatus of Claim 2 wherein said transmitter means includes means for transmitting a known set of symbols for training purposes and wherein said itiens for sensing the differences between said first and second sets of data includes means for developing said known symbol set as said first set, thereby to provide said detecting and demodulating means with a training cycle using a known symbol set. |

10. | The apparatus of Claim 9 wherein said transmitting means includes means for transmitting sequential packets of data with said known symbol set embedded at a predetermined position in a packer. 58 . |

11. | The apparatus of Claim 9 wherein said transmitting means includes means for developing a received data set of symbols as said first set. |

12. | The apparatus of Claim 1 wherein said transmitting means includes means for phase shift keying said transmitter. |

13. | The apparatus of Claim 12 wherein said phase shift keyed modulation is four phase. |

14. | The apparatus of Claim 1 wherein said transmitting means includes amplitude shift keying for the carrier thereof. |

15. | The apparatus of Claim 1 wherein the modulation of said carrier includes combined PSK/ASK modulation. |

16. | The apparatus of Claim 15 wherein said combined PSK/ASK modulation is quadratureamplitude modulation. |

17. | An underwater acoustic communications system for transmitting and receiving symbols comprising means for transmitting and receiving information between two laterally spaced locations, said information being transmitted in phase coherent form. |

18. | The system of Claim 17 wherein said receiving means includes means for removing channel induced interference. |

19. | The system of Claim 18 wherein said means for removing channel induced interference includes a lattice decision feedback equalizer. |

20. | The system of Claim 19 wherein said receiver means includes symbol sampling means and wherein said means for removing channel induced interference includes means for removing the effects of Doppler from received symbols and 59 means for matching symbol sampling intervals with received symbol sampling intervals. |

UTILIZING PHASE COHERENT COMMUNICATIONS FIELD OF INVENTION

This invention relates to underwater communications and more particularly to a system for optimizing digital communications through the utilization of both phase coherent modulation and demodulation along with specialized coding and decoding techniques involving combined equalization, phase estimation and symbol synchronization.

BACKGROUND OF THE INVENTION

Achieving reliable high data rate communications over long range underwater acoustic channels is achievable only if one can detect and rapidly account for the very rapid changes in the underwater acoustic channel. In the past acoustic communication has only been possible with slower incoherently demodulated frequency shift keying (FSK) . While coherent PSK systems have been used to transmit data, they have only been used in a vertical direction in deep water applications where no multipath or channel fluctuations occur. Assuming the harsh marine environment can be overcome, a high data rate digital underwater communications system has instant application to military surveillance, pollution monitoring, production oil field control, command and monitoring, remote sensing and even scuba diver communications. To date such applications are limited primarily due to signal fading and multipath problems as well as turbulence and Doppler induced artifacts, which severely limit realization of any practical system.

To understand the difficulties of underwater communication, it will be appreciated that the underwater acoustic channel is characterized as a time dispersive, rapidly fading channels, which in addition exhibits Doppler

effects. Also, a major obstacle for satisfactory synchronization is the time varying intersymbol interference (ISI) and Doppler shifts associated with moving vehicles.

As will be appreciated, underwater acoustic data telemetry is thus a taxing problem because many unique channel characteristics such as fading, extended multipath, and refractive properties of the sound channel preclude direct applications of classical communication techniques. Over the years there have been many attempts to design a reliable acoustic link, largely by grafting methods developed for other channels. Many of these approaches fail in the aquatic environment. Of particular interest is the failure of frequency shift keying to provide bandwidth efficiency for high data rates. The following describes both the harsh environment for underwater acoustic communications and several prior techniques attempting to combat the problems associated with the harsh environment.

I. ACOUSTIC CHANNEL BEHAVIOR

The ocean acoustic channel creates strong amplitude and phase fluctuations in acoustic transmissions. The fluctuations are induced by internal waves, turbulence, temperature gradients, density stratification, and related phenomena causing local perturbations in the sound speed. these interact with the transmitted wave fronts through diftractive and refractive effects, causing temporal, spatial, and frequency-dependent fluctuations in the received waveforms. In addition, there exist multiple propagation paths from transmitter to receiver in most underwater propagation geometries. In the deep ocean these are described as rays or wave guide modes, and in shallow water, also as reflections from discrete and distributed scatterers. Received signal fluctuations arise from medium fluctuation along a single path (micro ultipath) and time-variant

interference between several propagation paths (macromultipath) . The scintillation behavior and its effect on data transmission naturally decompose into single-path fading and the multipath effect consideration brought about by the dispersion relation and the effects of channel boundaries.

A. Single-Path Fluctuation The effects of fading channels on data transmission are well known. Amplitude and phase fluctuations increase the selection and performance of signaling techniques, for instance, MFSK.

The questions of primary interest are the types of ocean acoustic channels with fluctuation levels sufficiently low to permit coherent signaling, and the temporal, frequency, and space-dependence of the received pressure field. The telemetry system designer is driven to employ a coherent system for greater data throughput, but the sensitivity issues of coherently demodulated systems to channel fluctuations up until the present invention were thought to require more robust incoherent domodulation. Priorly it was thought that coherent signaling could be used only in applications where the fluctuation level and dynamics were sufficiently low to permit coherent carrier acquisitions and tracking. Thus it was thought that strong medium fluctuations precluded coherent carrier-phase tracking.

Acoustic fluctuation is a function of range and frequency. The principal fluctuation mechanisms over the long range deep water channel are internal waves governed by the Garret-Munk power spectrum and homogenous isotropic turbulence. Turbulence dominates the region above 10 kHz and under 10 km.

The above reflects typical fluctuation behavior. Extremal channel behavior is of interest to acoustic telemetry designers because the systems are designed to

operate under many channel conditions, and a system breakdown due to an infrequent but severe event is unacceptable.

While their requirements are tempered by past experiences of operating at sea, models of typical fluctuations are inadequate, and systems designed for average channel behavior suffer in overall performance and robustness. Given the lack of success of modeling, there is a requirement for a system which can accommodate the severe marine environment which is model independent.

B. Multipath

The relatively slow sound speed in the ocean gives rise to extended multipath structures. The SOFAR channel in the deep ocean and many coastal and harbor environments have characteristic reverberation times from tens of milliseconds to several seconds, and the time variant multipath must be recognized as a basic channel characteristic, present in all but few propagation paths of interest.

For instance, the SOFAR (sound ocean fixing and ranging) channel yields a number of distinct arrivals for source- receiver separations of one convergence zone or greater. A typical multipath spread is on the order of I s, with individual path RMS fluctuation of approximately 10 ms.

At short ranges, refections from objects and channel boundaries dominate the multipath; the problem becomes geometry-specific and no generic solutions are available. It is important to note that multipath itself is not the fundamental performance constraint for acoustic telemetry systems. Rather a single-path temporal fluctuations and multipath time stability are primary performance problems.

C. South Attenuation and Transmission Loss

Waveguide characteristics of the underwater channel introduce a strong spatial dependence into the received signal level for the deep-water channel, and for the shallow- water environment. Acoustic attenuation is governed by the

source-receiver separation, channel waveguide characteristics, and frequency-dependent absorption. While generic approximations for transmission loss (TL) and the channel transfer functions exist, today's numerical propagation modeling techniques are capable of accurate transmission loss, impulse response, and boundary-scattering transmission loss, impulse response, and boundary-scattering predictions. Careful source-receiver positioning can yield large (e.g., 40 dB) improvements in the received signal power. On the other hand, "shadow zones," i.e., regions with unusually high transmission loss, represent volumes from which acoustic telemetry is practically impossible. Note, sound absorption is the most stringent limitation on the carrier frequency and available system bandwidth, as rapid attenuation of higher frequencies imposes a maximum frequency limit for a telemetry system.

Transmission loss due to geometrical spreading and waveguide features introduces strong spatial and spectral dependence on the pressure level of the received waveforms. In fact, there are geometric configurations in many ocean channels where date telemetry is infeasible due to the excessive transmission loss from in situ sound velocity profiles and bottom bathymetry data can predict the occurrence and extent of these "shadow zones," guide system placement, and/or dictate times when a link can be expected to fail. Automatic repeat request, spatial and frequency diversity, as well as telemetry networking, can be used to overcome the transmission loss fluctuations, but lead to rather complex implementations. Spatial and spectral variability of the received signal level pose particular problems when the source and/or receiver are moving; for example, when communicating with a moving remotely operated vehicle (ROV) . The channel fluctuation then poses fundamental convergence problems to receiver equalizers and echo processors. Incidentally, Doppler shifts caused by relative motion are much simpler to

tract and compensate for than the spatial variability of the channel transfer function.

D. Ambient Noise Ambient ocean-noise influences the received signal-to- noise ration and largely controls transmitter power. It generally decreases in frequency over the range of interest, forcing the designer to operate as close to the attenuation limit as possible. In general, the low cutoff of the data band is determined by the ambient noise spectrum and the high point by absorption considerations. Inshore environments and marine worksites are as a rule much noisier than the deep ocean environment, and the system designer is face with selecting realistic worst-case performance conditions and robust criteria for the system. In the 10-20-kHz band used by many acoustic telemetry systems, the dominant noise-generating mechanism is due to resonant air bubbles introduced primarily by braking waves or rain. For instance, the observed 14.5 kHz resonance peak due to rain results from bubbles of 0.22 mm radius. A breaking wave induces a strong acoustic noise field in its vicinity; during significant wavebreaking activity, the ambient noise level can increase significantly, and the suspended bubbles slow the sound speed to create a near- surface waveguide which increases the resultant sound level at the surface. Receivers deployed near the surface are particularly amenable to wave-caused noise, as the attendant mooring or ship is often a cause of significant bubble action. For near horizontal paths, forward scattering and attenuation caused by the bubble layer are significant factors. Vertical propagation interference is largely due to bubble ambient noise. Propagation interference becomes an issue only when the receiver is enveloped in a bubble plume, which causes serious data degradation. This phenomenon is particularly noticeable when operating from a

maneuvering ship, such as tracking and communicating with a fast-moving ROV.

The above littany of problems with underwater acoustic communications explains in part why prior systems for underwater communications have failed to provide reliable underwater communications a t sufficiently high data rates.

There is therefore a need for a robust acoustic telemetry system, designed with careful consideration to channel characteristics. Grafting communication techniques developed for more benign channels invariably results in unacceptable sensitivity to realistic channel behavior.

II. DATA TRANSMISSION SYSTEMS

This section explores telemetry techniques required for a robust data link designed for realistic ocean channels. The channel characteristics, and hence the system designs, can be grouped into three categories.

A. Lonq-Rancfe Systems Long-range systems from 20 to 2000-km range in deep water have an upper frequency limit between 500 Hz to 10 kHz, excess of 190 dB μ-Pa. The channel-phase stability over many propagation geometries in this range is rather good, and phase-coherent methods can be used. Generally, the main problem is transmitting enough power to overcome the high transmission loss and using signal coding to maximize the received signal reliability per bit. The long-range acoustic channel is a very complex waveguide; the high spatial TL variability requires either that the system be operated in regions where the channel fluctuations are low, or that real¬ time channel nowcasting and forecasting models be integrated into system operation.

The classical sonar equation is a useful first design check. For a 1000-km-deep-water, 1 b/s telemetry system at 220 Hz, it is given by

SNR = SL-αR - TL - NL 0 = 190 - 10 - 120 - 60 where a 100-w source level (SL) and an ambient noise level (NL) of to dB re uPa are assumed. The attenuation loss xR at this frequency and range is 10 dB. The resulting bit SNR (for a 1 b/s system) along any single-ray path is 0 dB, and the system is on the operational threshold. Considering the entire arrival of some 20 rays increases the SNR by 26 dB, but only if the receiver is capable of coherently processing the multiple arrivals. As the ocean multipath structure is generally quire dynamic, this is not a simple task. For example, an adaptive recursive least squares (RLS) equalizer is likely to encounter convergence problems when a channel impulse response changes significantly in less than 10 impulse response durations, and this bound is often approached by ocean channels. Also, the SNR per path available is marginally adequate to insure equalizer convergence. The bit SNR can be improved by using directive arrays at the transmitter and/or receiver. In practice, 20 dB or more of array gain is easily attainable, although the hardware and associated pointing issues make for more complex systems. Using narrow transmitter arrays allows use of a single eigenray path for propagation and alleviates the channel equalizer and multipath problems, but the transmitter needs to know and update the eigenray direction.

B. Medium-Range Shallow Water Systems Medium-range systems operate in the range of 1 to 10 km, and are often required to operate in shallow water and in the presence of an extended time-varying multipath. The upper- frequency limit ranges from 10 to 100 kHz, and the channel is fully saturated, with random phase and Rayleigh amplitude fluctuation. Medium-range systems are often asked to operate with large source/receiver velocities in enclosed areas with extensive multipath structures where the line-of-sight path does not constitute a principal arrival, and in the presence

of high noise levels, such as may be caused by nearby ship traffic or the bustle or a marine worksite.

The performance limitations of medium range systems are due to synchronization and equalization. 1) Synchronization: The synchronizer functions to provide a bit start-time reference to the receiver. Many communication protocols rely on the data stream itself to provide synchronization. A least-squares optimal technique for synchronization tracking is the delay lock look (DLL) , and the device is implemented in many demanding communication systems. Its performance analysis for the AWGN environment with both coherent reception and incoherent reception is well understood. The principal areas of concern are the tracking error variance, mean time to lose lock (MTTLL) , and the mean lock acquisition time.

Channel multipath poses difficult problems to the synchronizer system, particularly the time-variant, dynamic multipath structures typically encountered in the ocean. If there is no discernable first or "principal" arrival, the definition of a single time of arrival instant can be problematic. For example, consider the case of two distinct, independently fading arrivals; there are several plausible ways of representing the synchronization instant, such as the first arrival, largest arrival, least-squares amplitude- weighted average of the two arrival times, etc. The synchronization choice must reflect the operation requirements of the later receiver stages, as it directly affects the equalizer and demodulator performance, among others. The synchronizer generally needs to be preceded or operate in conjunction with a multipath estimator and/or equalizer. As will be discussed, synchronizers with adaptive equalizers and the joint estimation of both sets of parameters is a part of this invention.

The classical solution is to synchronize on the first arrival. Most equalizer derivations assume synchronization on the first arrival, and a formulation for time-delay

estimation in the presence of multipath exists, assuming a stable first arrival. A problem occurs if the first arrival undergoes an extended fade or disappears entirely.

Synchronizing on a weighted sum of all the arrivals does produce a stable time-delay estimate, but a change in any single path affects the entire estimate, and the impulse- response dynamics are accentuated, leading to equalizer convergence problems.

Synchronizing on a principal arrival is equivalent to tracking the first arrival, and system performance is improved if the tracked arrival is selected as the most stable component of the impulse response. Tracking multiple components of the impulse response independently, with the goal of providing a stable estimate in the event of a principal path disappearance, is a promising method.

2) Equalization and Multipath Processing: Adaptive channel equalization was developed for use on telephone lines that are fundamentally different from the ocean acoustic channel, because their impulse response is relatively stationary in time and there are no fluctuations in the received signal. A straightforward application of an adaptive equalizer is likely to encounter equalizer convergence problems as it tries to keep up with the dynamic ocean multipath field. The convergence rate of the Kal an equalizer, generally recognized as the fastest converging adaptive equalizer, is given by

e _{a+ }ι = ι ^{~ }- _{P }N _{r } ^{€ }* ^{+ } pNTΛ ^{e, } OPT

where p is the peak-to-rms-eigenvalue ratio of the equalizer input covariance matrix, and Ν is the number of data frames affected by the multipath. During the convergence period, the equalizer is in a "training" mode, operating with a known

data sequence. In practice, the equalizer requires at least 10 iterations to converge, with each iteration requiring roughly one impulse-response data duration. A rough test of the Kalman equalizer suitability is whether the channel changes with a fluctuation rate faster than ten impulse response durations. Unfortunately, this condition often occurs in underwater acoustics, particularly in moving source-moving receiver implementations in shallow water. The equalizer formulation also assumes that the channel propagation time is fixed; i.e., that there is an unambiguous synchronization time to which the equalizer is referenced. Again, this assumption is often not valid.

The fundamental limit to equalizer use is the algorithm convergence rate. In practice, even the most complex equalizers are realizable on currently available hardware. This encourages exploring of algorithms that are considered too computationally intensive for other uses. In particular, ML equalization techniques are capable of high-resolution parameter estimation from short data sequences, and relatively efficient computational methods for ML equalizer implementation exist as seen in the following articles: M. Feder and E. Weinstein, "Parameter estimation of superimposed signals using the EM algorithm," IEEE Trans. Acoust. , Speech, Signal Processing, vol. 36, pp. 477-489, Apr. 1988 and M. Segal and E. Weinstein, "Spatial and spectral parameter estimation of multiple source signals," in Proc. ICASSP '89 (Glasgow, UK), Apr. 1989, pp. 2665-2668.

Equalization and echo processing in a slowly fading multipath channel can yield a data improvement over an equivalent channel without multipath by taking advantage of the implicit diversity inherent in independent signal fluctuations along each ocean path. An early example for this behavior for the case where multipath does not cause intersymbol interference is the RAKE receiver. A question of current concern is the definition of a channel-stability threshold below which optimal multipath processing of an ISI

channel yields performance superior to the system employing a single arrival for example, through the angle of arrival discrimination.

C. Short-Range Systems This section comprises the acoustic channels with relatively mild phase fluctuations over which transmission methods developed for telephone channels are feasible. Such channels encompass many vertical deep-water paths and very short-range (less than 200 m) horizontal paths. In this case, relatively simple techniques yield high data rates, but the resultant systems are susceptible to phase fluctuations and dynamic multipath largely because of carrier phase- tracking problems.

In summary, the two principal impediments to underwater acoustic telemetry are the spatial variability of the acoustic pressure field in the channel, and the channel temporal fluctuation rate. this is one of the few communication channels where the channel characteristics do not change slowly compared to the symbol rate. Many other channel features such as the details of the amplitude/phase scintillation and the difficulty of frame synchronization in a spread channel are problems.

D. Coherent Modulated Systems In the past, coherent modulated systems suffered significantly from channel fluctuations. As will be appreciated, coherent modulated systems fall into two categories: The very short-range systems where several hundred kHz of bandwidth is available, and the long-range ocean-basis systems where the bandwidth is limited to hundreds of Hz and the system is severely power-limited. While vertical or near-vertical deep-ocean paths can support coherently modulated telemetry, at least under normal channel conditions, until the present invention, coherent modulated horizontally oriented systems could not be readily

implemented to operate at high data rates in the presence of even moderate channel fluctuation level.

Coherent system performance in fluctuating channels has been a subject of much research and while rigorous performance bounds are not available, as will be seen, the subject invention describes an effective robust system that not only is possible but has been implemented.

Moreover, while long-range acoustic data telemetry suffers from high-power requirements to overcome relatively high ambient-noise levels and transmission loss; and while in practice, it is often simpler to deploy a surface- penetrating line and a high-speed satellite link, the subject system in large part solves the power-related problems associated with long range such that the transmit power requirement can be substantially reduced.

SUMMARY OF THE INVENTION

In order to achieve much improved underwater communications in an underwater acoustic communications system, high data rates are achieved through the use of coherent modulation and demodulation made possible through the use of rapid Doppler removal, a specialized sample timing control technique and decision feedback equalization including feedforward and feedback equalizers. The combined use of these techniques dramatically increases data rates by one and sometimes two orders of magnitude over traditional slower FSK systems. As one example, in the Code Alert communication system for submarines, the FSK symbol rate could not exceed 10 bits/second due to acoustic channel behavior. The subject system on the other hand has demonstrated at least in order of magnitude improvement for narrow bandwidth. the subject system successfully combats fading and multipath problems associated with a rapidly changing underwater acoustic channel that produces intersymbol interference and makes timing optimization for

the sampling of incoming data difficult. The most troublesome additional problems overcome by the subject system are the effects of turbulence and relative motion between transmitter and receiver causing unwanted Doppler shifts.

In one embodiment, rather than using traditional FSK, phase shift keying (PSK) is used. The result of using PSK and the above signal processing techniques within the data receiver is increased reliability, exceptionally high data rates, a power requirement reduced by 5, and about 10 times the bandwidth efficiency. In one embodiment rapid convergence for the equalizers so that they can track rapid channel change is made possible by the addition of noise filtering and working at baseband, in combination with rapid Doppler removal using a second order phase locked loop, and sample timing control using a timing synchronizer. The synchronizer is coupled to an interpolator and resampler for digitally adjusting the sampling interval.

Specifically, in one embodiment an input signal containing the data is filtered by a bandpass filter to remove noise, with the analog signal being converted into a digital signal after which the carrier is removed to provide a baseband signal.

The baseband signal is sampled by a sampling system which adjusts the sampling rate to correspond to the detected data rate. This is accomplished through the use of a synchronizing system controlled by a feedforward equalizer, and is a first order approach at removing the effects of Doppler shift. In operation, if the intersymbol spacing is stretched out because a receiver is moving away from the transmitter, the sample rate is slowed down such that the sampling interval matches the time between received symbols.

In a digital system changing the sampling interval is anon-trivial problem. It is solved in the subject system through the use of an interpolator and resampler which operates as follows. It one seeks to elongate the sampling

interval to match the stretched out interval between received symbols, the interpolator interpolates with a larger interpolating constant and resamples, with the desired result being a constant amount of information per symbol. In a typical 4 phase PSK system, at minimum two samples per symbol are required, although this number can increase depending on the application.

The data rate of the incoming signal is detected by a feedforward equalizer in the form of a transversal filter, with its taps updated using the RLS algorithm described by John G. Proakis in a paper entitled "Adaptive Equalization Techniques for Acoustic Telemetry Channels", IEE Jour, of Oceanic Engineering, Vol. 16, No. 1, January 1991, pps. 26- 27, Figures 7 and 8 and Table V, which describes both feedforward and feedback RLS Lattice DFE algorithms. This article incorporated herein by reference and is available as Appendix A hereto.

The feedforward equalizer in combination with the sampling interval control circuit removes as much multipath and Doppler as it can. However, there is still residual Doppler which must be eliminated; and for this purpose a Doppler estimator is employed to measure the residual Doppler and remove it. In one embodiment the Doppler estimator uses a standard second order phase locked loop (PLL) algorithm with its output used to directly cancel out Doppler induced phase errors in the sampled input signal.

Having removed Doppler from consideration, a feedback equalizer is used to cancel the intersymbol interference from previously detected symbols. The error signal used to adjust the coefficients of the feedback equalizer results in equalizer coefficients of the feedback equalizer results in equalizer coefficients that are estimates of the channel- induced intersymbol interference. It will be noted that channel induced interference refers to changes in phase and amplitude of received signals caused by multipath, thermals, wave action, turbulence and speed of propagation changes.

The error signal is generated as a result of the convergence of the equalizer as it operates first on a known symbol set in a training cycle or mode, and thereafter on the detected symbols themselves. In order to initialize the receiver with a training sequence, the transmitted data is transmitted in packets, with 20-50 training symbols preceding the data. The feedback equalizer is first provided with coefficients based on the comparison of received data corresponding to the known symbol set, with the known symbol set stored at the receiver. The coefficient adjustment algorithm is based on a recursive least squares (RLS) criterion and is described in the paper appended hereto as Appendix A. The RLS algorithm is a coputationally intensive and complex method for adjusting the equalizer coefficients that provides rapid convergence compared with the well-known simpler and slower-converging LMS algorithm.

The feedforward equalizer is also in the form of a transversal filter updated using the aforementioned RLS algorithm.

Both equalizers operate on previously detected signals in the decision-directed mode and on known data symbols in the training mode. The tap weights of both equalizers form the composite tap-weight vector which is updated by the overall error in the RLS algorithm. The data vector it uses consists of the input signal samples with corrected phase and previously detected signals.

The entire feedforward and feedback equalizer system provides substantially error free data to a symbol detector used as a decision device to decide finally what phase was actually transmitted.

For instance, if the phases are 0 ^{° }, 90», I80o, and 270., then a received signal with 10 _{° } phase is considered to be 0«. This phase jitter corrected output is then coupled to a standard decoder for further error detection and correction.

As an example of the improvement associated with phase coherent modulation in combination with improved timing synchronization, in a long-range scenario where only 10 bits/second could reliably be transmitted with the subject system this is raised to 660 bits/second over 110 nautical miles. The bit rate goes up dramatically for short range to 20,000 bits/second even though short range, shallow depth channels have severe problems due to turbulence, multipath and Doppler. Not only is the data rate improved by an order of magnitude, power requirements are dropped to one-fifth, whereas bandwidth efficiencies are improved by a factor of ten.

Further improvements in performance are achieved by the use of coding and decoding. In particular, coded modulation in which the code is embedded or integrated into the modulated symbols at the modulator provides an additional power savings of 3dB to 6dB without any reduction in the data rate. Coding and decoding may also be used to provide conventional error detection and error correction. The latter form of coding and decoding also provides a power savings but at a sacrifice, i.e., a reduced data rate.

From the point of view of combined optimization of synchronization and equalization techniques, the optimum maximum likelihood receiver for joint estimation of synchronization parameters and the data sequence is difficult to implement in the case of a fading, time dispersive channel. Besides requiring the complete knowledge of the channel impulse response, which not only is generally unknown, but is actually time varying, the complexity of such receiver grows exponentially with the length of the channel response, making it impractical for high symbol rates when the channel response spans tens of symbol intervals.

To circumvent these problems, the subject invention is directed to a receiver using a suboptimum structure with a decision feedback equalizer (DFE) . The performance of a DFE in the absence of decision errors is comparable to that of

an optimal, maximum likelihood (ML) sequence estimator. The equalizer tap weights are estimated jointly with the synchronization parameters using the minimum mean squared error (MSE) criterion. Since the parameters to be estimated are not constant in practice, the subject system operates in an adaptive, decision directed mode.

BRIEF DESCRIPTION OF THE DRAWINGS These and other features of the subject invention will be better understood in conjunction with the Detailed Description taken in conjunction with the Drawings of which

Figure 1 is a block diagram of the receiver structure permitting improvements in underwater data communications, indicating a feedforward section of an equalizer, a feedback section of the equalizer and generation of estimation error to provide an analog estimate of the data signal;

Figure 2 is a graphical diagram of an ensemble of channel responses at 110 nautical miles which is the result of RLS-estimation;

Figures 3A, B, C and D are graphs of the results for QPSK, 33 symbols per second, 80 nautical miles for receiver parameters N=8, M=2, λ = 0.99, Kθ _{j } - 0.01; Kθ _{2 } = 0.001;

Figures 4A, B, C, and D are graphs of the results for QPSK, 333 symbols/sec. , 110 nautical miles for receiver parameters N=40, M=10, λ = 0.99, Kθ, = 0.001, Kθ _{2 } = 0.001; Figure 5B is a block diagram of the Doppler estimator of the system illustrated in Figure 5A;

Figure 6 is a schematic diagram of the feedforward equalizer of Figure 5; and,

Figure 7 is a schematic diagram of the feedback equalizer of Figure 5.

DETAILED DESCRIPTION

The derivation of the receiver algorithm, and the experimental results of its application to the long range underwater acoustic (UWA) telemetry data is not presented.

Referring now to Figure 1, the data receiver 10 can in general be viewed as including an interpolator/resampling module 12 which is coupled to a feedforward equalizer 14 that is in turn coupled to a Doppler compensation node 16 fed via a Doppler estimator 18. The Doppler compensated output of node 16 is applied to one of the two inputs to an interference compensation node 20 driven by a feedback equalizer 22. The output of node 20 is coupled to a symbol detector 24 which serves as a decision device to provide a final determination of the phase of a signal so that accurate symbol determination can be made.

For a generalized perspective, the received signal, for a general class of linear modulations, is represented in its equivalent complex baseband form as

^{v }^- = Y, d _{n }h { t-nT-τ ) e + v( T) , t€T _{obs (1) } n

where [d„] is the data sequence, T is the symbol duration, h(t) is the overall channel impulse response, and v(t) is white Gaussian noise. It is initially assumed that the carrier phase θ symbol delay T and the channel response h(t) are constant during the observation interval T^. The structure of the receiver is shown in Figure 1. Since the channel is not known, the matched filter h* (-t) is omitted, and the received signal v(t) is sampled directly. Sampling at the equalizer input may be performed at the symbol rate, in which case the existence of an accurate symbol timing phase estimate is crucial for the satisfactory performance of the equalizer. On the other hand, a fractionally spaced (FS) equalizer, which uses a sampling interval smaller than the reciprocal of the signal bandwidth, is capable of synthesizing the optimal sampling instant, provided that the coarse synchronization exists. Although a FS equalizer is the present choice for implementation, for the sake of

generality the derivation the estimation of symbol delay is included.

The sequence of input signal samples is fed into the feedforward or linear part of the equalizer. After compensation for the carrier phase by the amount , the signal is fed into the feedback section (decision device and feedback equalizer) of the receiver. Let a' and b' denote the row vectors of N feedforward and M feedback equalizer taps respectively. the input signal is conveniently represented in vector notations v(n,f) = [v(nT + ϊi,T _{s } + τ)...v _{n }(nT - N _{2 }T _{S } + θ ) ] ^{τ }, where (.) ^{τ } and (.) ' denote transpose, and conjugate transpose respectively. The (analog) estimate of the data symbol is obtained as

d _{n } = a'v(n,f)e- ^{jδ } - b'd(n) (2)

where d,. = [d,.., ... d,.. _{M }] ^{τ } is the vector of M previous decisions which are currently stored in the feedback section of the equalizer. The decision d _{n } is obtained by quantizing the estimate d _{n } to the nearest symbol value. The estimation error is defined as e _{n } = d _{n }-d _{n }, and the optimization of the receiver parameters is performed through minimization of the MSE with respect to all the relevant parameters. Substituting the expression (2) for d _{n } in the expression for the MSE, it is shown that the MSE is given by

Differentiating the expression for MSE with respect to the equalizer coefficients a, b, and the synchronization parameters θ , f , results in the set of gradients

2E {a(n) e * _{n }) (4)

= - 21m { p _{n } ( d _{n } + q _{π }) *}} -ff = - 2ReiE {P ) (5) δτ

where p _{n } = a'γ(n,f)e ^{"jβ } is the output of the feedforward section with corrected phase, q _{n } = b'd(n) is the output of the feedback section, p _{n } = a'v(n, r)e ^{~j }* is the output of the feedforward section with the corrected phase, when its input is the time derivative of the received signal, v(t) , and d„ ^{= } P _{o } ~ i _{n }* ^{In } the decision directed mode, d _{n } should be substituted by d„.

Setting the gradients equal to zero results in the set of equations whose solution represents the jointly optimum receiver parameters. Although this solution does not exist in the closed form, it could be obtained numerically. However, since the channel is actually time varying, so are the optimum values of the receiver parameters. Therefore, one seeks to obtain the solution to the above system of equations in a recursive manner. Then one can expect that once the algorithm has converged, it will continue to track the time variations of the channel. A commonly used form of an adaptive algorithm is obtained through the use of stochastic gradient approximation. The simplest form of this solution is the so-called LMS algorithm, in which each parameter is updated by the amount proportional to the instantaneous estimate of its gradient. Such an algorithm, however, may not be powerful enough to track all the fluctuations present in the underwater acoustic channel.

In order to design a robust algorithm that is suitable for the time variations of the underwater acoustic channel, several improvements are introduced. Considering first the synchronization parameters update, and in particular the update equation for the carrier phase estimate, with similar conclusions applying to the symbol delay estimate update due

to the similarities between the two equations, in order to obtain improved tracking capabilities of carrier phase estimate, a second order update equation for this parameter is introduced. This is obtained when it is recognized that the gradient of the MSE with respect to carrier phase estimate is proportional to the output of an equivalent phase detector. Indeed, if there were no ISI, the value of the MSE gradient with respect to θ would be proportional to sin(θ _{n } - 0 _{n }) , which represents exactly the phase detector output of a digital PLL. Based on the analogy with the digital PLL, but using the expression (5) , the equivalent phase detector output is defined as _{n } = Imfp^d,. + g _{n })*]. The second order carrier phase update equation is then given as

n θ _{Λ+ }ι = θ, ^{+ } *bιΦ-n ^{+ } *t∑Φ, (6) ι=0

where K _{Θ }-, K _{Θ2 } are the proportional and integral tracking constants. In the absence of ISI and decision errors, the synchronization parameters update equations describe the operation of classical second order synchronization loops. Here however, they are coupled with the process of equalization. In particular it is interesting to note that the MSE gradient with respect to θ requires knowledge both of the outputs of the feedforward and the feedback section of the equalizer, while in the case of marginal estimation it would require knowledge only of the input signal and the detected symbol.

In order to achieve faster convergence of the algorithm during relatively short training periods, the recursive least squares (RLS) estimation criterion is used for the equalizer tap coefficients update. To accommodate for the time variations of the channel, windowing of the data can be introduced through a forgetting factor, denoted by λ.

Looking at the structure of the receiver, it can be seen that it allows carrier phase recovery to take place after the feedforward equalization, thus eliminating the problem of delay in the carrier phase estimate. However, this is not the case with the symbol delay estimation, with the consequence of having residual timing jitter. An FS equalizer, by virtue of being insensitive to the choice of the sampling instant, does not require estimation of the precise symbol timing, and automatically overcomes this problem. The algorithm operates only on 2 samples per symbol interval, and since no feedback to the analog part of the receiver is required, it is well suited for an all digital implementation. However, the use of finer fractional tap spacing is also possible, although it is unnecessary. The presented system was tested and proved efficient on the real long range underwater acoustic telemetry data. Some of the results are presented hereinafter.

EXPERIMENTAL RESULTS

The analyses were preformed using data collected during an experiment conducted by the Woods Hole Oceanographic

Institution off the coast of California in January 1991. The modulation format used in the experiment is QPSK and 8-QAM, with data rates ranging from 3 to 300 symbols per second.

In the experiment a 100 watt transmitter at a carrier frequency of 1 kHz transmitted packets with an intersymbol interval of 1 msec to 1 sec corresponding to a maximum data rate of 1000 bits/sec, with nominal sampling rate of 4 kHz.

Bandwidth efficiency is achieved by cosine roll-off pulse shaping of the signal at the transmitter by a cosine roll-off filter with roll-off factor 0.5 and truncation length ± 2 symbol intervals. The data were transmitted over ranges of approximately 40-140 nautical miles, and received with a vertical hydrophone array of 12 sensors spanning depth of 1500m.

In order to gain insight into the multipath and fading characteristics of the channel, a series of analyses with channel estimation was first performed. Figure 2 represents an example of the ensemble of channel impulse responses obtained by an RLS-based adaptive channel estimator. It refers to the transmission over 110 nautical miles, and shows that the overall multipath spread is on the order of 60ms, while significant time variations of the channel response due to fading can occur in time intervals less than 10s. Two examples of different rate and range transmissions were chosen, for which the results of the application of the presented algorithm are shown in Figures 3 and 4. Figure 3 shows the results obtained with QPSK (four phase PSK) signals transmitted at the rate of 33 symbols per second, over 80 nautical miles. The first plot represents the scatter plot of the received signal after compensation for the constant Doppler frequency shift in the received signal. Although there is not much ISI present here, the phase fluctuations are considerable. The SNR in this case was on the order of 25dB. Shown in the remaining plots are the mean squared error, which indicates the convergence of the algorithm, and the carrier phase estimate, both as a function of time measured in symbol intervals. It is seen that significant changes in the carrier phase occur in time intervals of only couple of symbols. The last plot is the scatter plot of the output signal on which the decisions are performed, in this case with no errors. The fractional spacing of T/2 was used in all the cases, since it is sufficient for the signal bandwidth of 3/4T. We have found by trial that the choice of the RLS forgetting factor λ = 0.99, and the choice of the integral phase tracking constant 10 times smaller than the proportional tracking constant, resulted in satisfactory performance. Figure 4 presents results for QPSK signal transmitted at the rate 333 symbols per second over 110 nautical miles.

In this case the eye is initially completely closed due to the EASE, phase fluctuations and noise. The SNR is on the order of 15dB. Since the signaling rate is relatively high, the EASE spans at least 20 symbol intervals. The algorithm successfully copes both with the EASE and phase fluctuations, as can be seen from the output scatter plot.

Satisfactory results were also obtained with 8QAM and 8 PSK signal constellations.

Noise levels in general are higher at lower depths, as well as for longer distances. However, although the noise level increases with range, so does the number of multiple arrivals, and it was observed that a correctly positioned receiver may actually perform better at longer distances due to the fact that it makes use of the implicit diversity present in the multipath propagation.

Improved performance with respect to noise and fading can also be achieved through the use of spatial diversity, and the proposed algorithm is suitable for the extension to the multichannel case in which signals from multiple hydrophones are combined.

In order to achieve reliable coherent communications over long range underwater acoustic channels, a receiver algorithm which jointly performs synchronization and decision feedback equalization of the received signal is presented hereinafter. The algorithm was applied to the experimental data transmitted at rates as high as 333 symbols per second over ranges up to 140 nautical miles. The results assert the feasibility of coherent communications over underwater acoustic channels, and demonstrate the suitability of the proposed algorithm for the application in fading multipath channels with long impulse responses and phase instabilities.

DETAILED EMBODIMENT

Referred now to Figure 5A, a block diagram of one embodiment of the subject system is presented in which a

transmitter section 50 is provided with a data source 52 coupled to an encoder 54 which is in turn coupled to a modulator 56 that is coupled to transmitter 58. The output of transmitter 58 is coupled to a hydrophone 60 for the projection of acoustic data into the water in a generally horizontal direction. Encoder 54 is provided with a known symbol set 55 utilized for training purposes, or with the output of the data source 52.

The encoder 54 encodes the data to produce tan integrated coded modulation signal at the output of the modulator, with decoding performed at the receiver as shown in Scenario A. The encoder 54 may also be used to provide redundancy for conventional error detection and error correction at the receiver as shown in Scenario B. With respect to the receiver, a hydrophone 62 is coupled to a band pass filter 64, which is in turn coupled to an analog-to-digital converter 66 that is utilized to sample the analog signal which has been previously filtered. The output of the analog-to-digital converter is coupled to a circuit 68 which removes the carrier to provide a baseband signal that is coupled to a sample timing and synchronization module 70. This module includes a timing synchronizer 72 and an interpolator/resampler 74 for setting the sampling interval to the detected interval that has been sensed by a feedforward equalizer 76 during its normal operation.

Referring now back to Figure 5A, the output of the feedforward equalizer is provided through a Doppler compensation multiplier 78, node 16 of Figure 1, as one input to a Doppler Estimator 84. Multiplier 78 is also coupled through an interference cancelling summing junction 80, node 20 of Figure 1, and through a differential summing junction 82 to the other of the inputs to Doppler estimator 84. One input to summing junction 82 is the known symbol set 56 which is compared to a coarsely compensated signal. One embodiment of the Doppler estimator is shown in Figure 5B.

The output of summing junction 82 is an error signal coupled to a coefficient generator 86 which generates adjusted coefficients in accordance with the RLS algorithm. The coefficient update equation may be expressed as

c (n) = c (n-1) - k (n) e (n)

where e (n) is the error signal, c (n) is the updated combined equalizer coefficient vector, c (n-1) is the previous coefficient vector and k (n) is a vector that is computed based on the RLS criterion as described in Appendix A.

The corrected or adjusted coefficients are applied as tap weights to feedforward equalizer 76 and a feedback equalizer 88 coupled to the output of a symbol detector module 90 that derives its output from summing junction 80. Note that junction 80 is coupled directly to a data decoder 92 in the case of Scenario A for embedded coded modulation symbols, whereas the input to decoder 92 is from symbol detector 90 for Scenario B for conventional coded transmission. After the training sequence, a switch 94 switches the corresponding input of junction 82 to the output of symbol detector 90 to receive detected symbols as opposed to the known symbol set.

Note that bandpass filter 64 is a common bandpass filter set with a passband of 600 Hz in one embodiment. The filter is designed to passed the received signal and the bandwidth of the noised to that which falls within the signal frequency band, in one embodiment 700-1300 Hz.

Analog-to-digital converter 66 is a conventional devise used to sample the signal at a rate of at least twice the signal bandwidth, W. Typically the signal is sampled at four samples for a transmitted symbol, although this number can be higher.

The carrier removal circuit 68 translates the signal from a passband signal to a baseband signal by multiplying the passband signal with the sine and cosine of the carrier followed by lowpass filtering of each of the product signals. From this point on, the signal is treated as complex valued, where the real part is the output of the cosine demodulator and the imaginary part is the output of the sine demodulator.

The reason for working at baseband is as that physical hardware for a baseband realization is simpler, more power efficient and compact. However, a totally equivalent signal demodulator operating at passband or at any intermediate frequency can be implemented by a person skilled in the art of modem design.

As to timing synchronization; this is divided into three tasks: initial acquisition/synchronization, coarse synchronization and synchronization.

Initial acquisition/synchronization is performed by matched filtering with a known Barker code. The code is transmitted as part of the data preamble. The filter peak output is used to align the data sequence and assure the principal signal arrival coincides with the first tap of the feedforward equalizer 76.

Coarse synchronization is performed by adaptive interpolator/resampler 74 which decreases the data (sample)_ rate when detecting a travel time increase, and increases the rate when travel time shortens. The interpolation rate is determined by the timing synchronizer 72 which uses the tap structure of the feedforward equalizer 76 as input.

Fine synchronization is accomplished by the fractionally spaced feedforward equalizer, the algorithm of which adjusts its tap coefficients to compensate for minor delay fluctuations.

Interpolator/resampler 74 functions as follows: Typical interpolation methods include linear, quadratic, and sin (x) /x interpolation. The objective of the interpolator/resampler is to change input data rate, in

samples/second, without compromising data quality. For this application, data rate changes are typically less than 10% of the data rate.

Timing synchronizer 72 is configured as follows: Timing synchronizer sets the interpolator/resampler rate by monitoring the main or largest value of the feedforward equalizer. If the main tap is slightly delayed, the synchronizer increases the interpolator/resampler rate in order to advance the main tap back into equilibrium. As to Doppler estimator 84, this computes the carrier phase estimate once per symbol interval. The current estimate is updated by adding two terms: a term proportional to the phase error signal, and a term proportional to the sum of previous phase error signals. The phase error signal is obtained as Im[pn(pn + en)*], where en is the overall error and pn is the output of the feedforward equalizer 76 with corrected phase. Note that the output of the Doppler estimator is applied back to cancel the residual Doppler. The computational algorithm is a second order phase-locked- loop with the loop coefficients K, and K _{2 } selected according to channel fluctuation rate. Note that Figure 5B illustrates a typical implementation.

Feedforward equalizer 76 is shown in Figure 6 and is described in the aforementioned article by John G. Proakis. Note that a _{i } , a _{2 } a _{n } are the equalizer coefficients and that the output of the filter is compute once for every two input samples for T/2 (T-symbol duration) spaced samples of input signal. This is a transversal filter with total number of Nj + N _{2 } + 1 taps, where TN _{2 } is the delay it introduces in order to compensate for the ISI of future symbols. Its tap weights are updated together with those of the feedback filter using the RLS algorithm. Its coefficient updating algorithm as given previously is a (n) = a (n-1) + k (n) e (n) and its output is given by the equation a'(n) v (n,f). The purpose of the feedforward equalizer is as follows: The role of the feedforward equalizer is to weight and coherently

combine the received signal multipath components and, simultaneously, to minimize the effect of intersymbol interference from future symbols, sometimes called precursors, on the current symbol that is being estimated. Feedback equalizer 88 is shown in Figure 7 where b,, b _{2 } -

— b _{m } are the coefficients. Note, the feedback equalizer inputs are the previously detected symbols, with its output being an estimate of the ISI from past symbols. The purpose of the feedback equalizer is to eliminate the intersymbol interference due to previously detected symbols from the current symbol being estimated. Its tap coefficients adapt to the ISI values contained in the channel postcursors, sometimes called the tail of the channel response.

Decoder 92 is designed to match the encoding process produced at the transmitting end of the system. When coded modulation is used, in which the coding is embedded in the modulation, the decoder operates in Scenario A and takes its input from the output of the summing device 80. In this mode, the decoder decodes the transmitted data symbols based on computation of Euclidean distance metrics for the possible transmitted sequence of symbols. When conventional coding is performed for error detection and error correction, the decoder operates in Scenario B and takes its input from the output of the symbol detector. In this mode, the decoder decodes the data symbols based on computation of Hamming distance, which is conventionally used in decoding of block and convolutional codes.

The symbol detector 90 takes the input data estimate from the summing device 80 and maps each data symbol estimate to the closest (in Euclidean distance) possible transmitted symbol. For example, if 4-phase PSK modulation is used with possible transmitted phase 0°, 90°, 180°, 270°; a symbol estimate that falls in the range of 45° to 135° is mapped to 90°, and estimate that falls in the range of 135° to 225° is mapped to 180°, one that falls in the range of 225° to 315° is mapped to 270°; and an estimate that falls in the range

of 315° to 45° is mapped to 0°. The output decisions from the symbol detector are fed to the decoder which performs conventional error detection and error correction by using the redundancy in the transmitted symbols inserted by the encoder at the transmitter.

It will be appreciated that the overall equalizer including feedforward and feedback functions is known as a decision-feedback equalizer (DFE) . While the above description has included implementation of the equalizer in terms of a transversal filter, including a tapped delay line, the subject system may be implemented with a lattice DFE described in the publication of Appendix A hereto. It is also described in the book authored by John Proakis entitled "Digital Communications", McGraw Hill, Second Edition, 1989, and particularly in Chapter 6 thereof.

The program listing, written in MATLAB, for the system depicted in Figure 5A is included herewith as Appendix B. A multichannel version of the subject system is included herewith as Appendix C. It will also be appreciated that the type of modulation signals includes all phase coherent modulation methods including phase shift keying, amplitude shift keying, and combined PSK/ASK, known as quadrature-amplitude modulation or QAM. Additionally, coded modulation, including block-coded and trellis-coded modulation may be used in the subject system. In both of these coded modulation schemes, the coding is embedded in the modulated symbols. These types of coding are widely used in all high speed telephone modems, and is discussed in the above book entitled "Digital Communications" in Chapter 5 thereof.

The subject system can of course utilize conventional error detection and error correction coding and decoding. This type of coding and decoding is routinely used in many communication systems. Typical codes include the Hamming codes and BCH codes, including Reed-Solomon codes.

Finally, the Barker code used for initial synchronization is but one of many possible sequences that may be used. Any sequence that has a large autocorrelation peak and very small side lobes is suitable. One example is the class of shift register sequences known as "m-sequences".

Having above indicated a preferred embodiment of the present invention, it will occur to those skilled in the art that modifications and alternatives can be practiced within the spirit of the invention only as indicated in the following claims.

APPENDIX A

Adaptive Equalization Techniques For Acoustic Telemetry Channels

John G. Proakis, Fellow, I E (Invited Paper)

Abstract — A tutorial review of adaptive equalization techniques for combating intersymbol interference in high-speed digital communica¬ tions over time-dispersive channels is given. Various equalizer structures and the associated adaptive algorithms, including both fractionally spaced and symbol-spaced equalizers, are presented. Also considered is the application of adaptive equalization techniques to underwater acous¬ tic telemetry channels.

Manuscript received June 18, 1990; revised September 25, 1990.

The author is with the Communications and Digital Signal Processing Research Center, Department of Electrical and Computer Engineering, Northeastern University, 360 Huntington Avenue, Boston, MA 02115.

IEEE Log Number 9040832.

- 33A -

I. INTRODUCTION

ADAPTIVE equalization techniques have been developed over the last two decades for high-speed, single-carrier serial transmission over wire line channels and radio channels such as microwave line-of-sight, troposcatter, and HF. Some of these techniques are also applicable to underwater acoustic telemetry channels, especially if they are characterized as under- spread; i.e., the product of the multipath spread and Doppler spread is less than unity. For such, channels, adaptive equaliza¬ tion provides the means for combating intersymbol interference arising from the time-dispersive characteristics of the channel and allows us to make efficient use of the available channel bandwidth.

Section II of this paper provides a tutorial review of adaptive equalization techniques for combating intersymbol interference in high-speed digital transmission over time-dispersive channels. Our treatment covers the various equalizer structures and associ¬ ated adaptive algorithms, including born fractionally spaced and symbol-spaced equalizers. The performance characteristics, the limitations, and the implementation complexities of the adaptive equalization algorithms are also described. Section III deals with the characteristics of underwater acoustic telemetry channels and their impact on the use of adaptive equalization. In Section IV we consider block-processing adaptive equalization methods which appear to be especially suitable for the rapid signal phase fluctuations that are frequently observed in medium-range acous¬ tic telemetry systems operating in shallow water. Section V presents our conclusions. π. SURVEY OF ADAPTIVE EQUALIZATION TECHNIQUES

Equalization techniques for combating intersymbol interfer¬ ence (ISI) on band-limited time-dispersive channels may be sudivided into two general types— linear and nonlinear equaliza¬ tion. Associated with each type of equalizer is one or more structures for implementing the equalizer. Furthermore, for each structure there is a class of algorithms that may be employed to adaptively adjust the equalizer parameters according to some specified performance criterion. Fig. 1 provides an overall cate¬ gorization of adaptive equalization techniques into types, struc¬ tures, and algorithms.

- 33B -

Equalizer

Types Nonlinear

Linear 1

ML Symbol

DFE Detector MLSE

Structures _£ i

Transversal

Transversal Lattice Transversal Lattice Channel Estimator

I Algorithms ♦

LMS LMS

Gradient Gradient LMS RLS RLS RLS RLS RLS Fast RLS Fast RLS Fast RLS Square - Root RLS Square - Root RLS Square - Root RLS

Fig. 1. Equalizer types, structures, and algorithms.

Fig. 2. Adaptive linear FIR equalizer with LMS algorithm.

- 34 -

A. Linear Equalization Techniques

A linear equalizer may be implemented as a finite-duration impulse response (FIR) filter (also called a transversal filter) with adjustable coefficients. The adjustment of the equalizer coefficients is usually performed adaptively during the transmis¬ sion of information by using the decisions at the output of the detector in forming the error signal for the adaptation, as shown in Fig. 2. For symbol error rates below 10 ^{" 2 }, the occasional errors made by the detector have a negligible effect on the performance of the equalizer. During the start-up period, a short known sequence of symbols is transmitted for the purpose of initial adjustment of the equalizer coefficients.

The criterion most commonly used in the optimization of the equalizer coefficients is the minimization of the mean square error (MSE) between the desired equalizer output and the actual equalizer output. The minimization of the MSE results in the optimum Wiener filter solution for the coefficient vector, which may be expressed as _{p }^ r- 's (i) where T is the autocorrelation matrix of the vector of signal samples in the equalizer at any given time instant, and £ is the vector of cross correlations between the desired data symbol and signal samples in the equalizer.

In practice, the autocorrelation matrix T and the cross-corre¬ lation vector £ are not known explicitly. However, they can be estimated as time averages from the transmission of a known data sequence and substituted in (1) in place of the ensemble averages T and £ in order to solve for the coefficient vector.

Alternatively, the minimization of the MSE may be accom¬ plished recursively by use of the stochastic gradient algorithm introduced by Widrow [1], called the LMS algorithm. This algorithm is described by the coefficient update equation:

C( t) = C( t - l) + A e{ t) Y*{ t) , = 0, 1 , ^{• • } - (2)

- 34A - where C(/) is the vector of the equalizer coefficients at the iteration index , Y(t) represents the signal vector for the signal samples stored in the FIR equalizer at the iteration index , e{t) is the error signal which is defined as the difference between the transmitted symbol /(/) and its corresponding estimate /( ) at the output of the equalizer, and Δ is the step-size parameter which controls the rate of adjustment. The asterisk on Y*(t) signifies the complex conjugate of Y{t). Fig. 2 illustrates the linear FIR equalizer in which the coefficients are adjusted ac¬ cording to the LMS algorithm given by (1). The symbol z ^{- 1 } denotes a unit sample delay.

It is well known [2, chap. 6] that the step-size parameter Δ controls the rate of adaptation of the equalizer and stability of the LMS algorithm. For stability, 0 < Δ < 2/ _{nax } , where λ^ is the largest eigenvalue of the signal covariance matrix. A choice of Δ just below the upper limit provides rapid conver¬ gence, but it also introduces large fluctuations in the equalizer coefficients during steady-state operation. These fluctuations constitute a form of self-noise whose variance increases with an increase in Δ. Consequently, the choice of Δ involves a trade off ^{" } between rapid convergence and the desire to keep the vari¬ ance of the self-noise small.

The convergence rate of the LMS algorithm is slow due to the fact that there is only a single parameter, namely, Δ, that controls the rate of adaptation. A faster converging algorithm is obtained if we employ a recursive least squares (RLS) criterion for adjustment of the equalizer coefficients. For the linear FIR equalizer, the RLS algorithm that is obtained from the minimiza¬ tion of the sum of exponentially weighted squared errors, i.e.,

_{< }? = ∑ w'-" | /(π) - /» | ^{2 } n =

may be expressed as [2, chap. 6]

CN( ') = C _{N }{t - 1) + P _{N }(t) Y (t)e{t) (3)

- 34B -

where I(t) is the estimate of the symbol /(/) at the output of the equalizer, C _{N }' (t) denotes the transpose of C _{N }(t), and

'(') = '(') ^{" } (') (4)

Number of iterations

Fig. 3. Comparison of convergence between LMS and RLS (Kalman) algorithms.

TABLE I CONVENTIONAL RLS (KALMAN) ALGORITHM

Update inverse of the correlation matrix: 1 p _{N }(0 = -[P _{N }υ - i) - κ _{N } ) Y _{N }' {t)p _{N } - D]

Update coefficients:

C _{N }{t) = C _{N }(t - 1) + K _{N }(t)e _{N }(t) = C _{N }(t - 1) + P _{N }(t) Yfi(t)e _{N }(t)

^{P }N( *) = - w

(5)

- 34C -

The exponential weighting factor w is selected to be in the range, 0 < w < 1. It provides a fading memory in the estima¬ tion of the optimum equalizer coefficients. P _{N }(t) is an (N x N) square matrix which is the inverse of the data autocorrelation matrix,

Initially, P _{N }( ) may be selected to be proportional to the identity matrix. Table I summarizes this RLS algorithm, which we call the "conventional RLS algorithm." Fig. 3 illustrates a compari¬ son of the convergence rate of the RLS and LMS algorithms for an equalizer of length, N = 11 , and a channel with a small amount of ISI. We note that the difference in the convergence rate is very significant. Typically, the RLS algorithm converges in about 5 to ION iterations (symbol intervals) at signal-to-noise ratios of 10 to 15 dB per bit.

The recursive update equation for the matrix P _{N }(t) given by (5) has poor numerical properties. For this reason, other algo¬ rithms with better numerical properties have been derived which are based on a square-root factorization of P _{N }(t), as P _{N }(t) = U(t)D(t)U'(i), where U{t) is an upper triangular matrix, and D{t) is a diagonal matrix. Such algorithms are called "square- root RLS algorithms" [13], [38]. These algorithms update the matrix U{t) directly without computing P _{N }{t) explicitly and have a computational complexity proportional to N ^{2 }.

RLS equalization algorithms for a transversal FIR equalizer with computational complexity proportional to N have also been devised. Algorithms in this class may be derived in a variety of

35 -

- 35A -

TABLE π FAST RLS (KALMAN) ALGORITHM

ways, as shown in the literature [2] -[5], and are called "fast RLS algorithms." One relatively straight forward derivation, given in [2, chap. 6], stems from the RLS lattice algorithm, which is described below. This fast RLS algorithm, given in Table II, has a computational complexity of 9/V + 3 complex multiplications and divisions per input signal sample. Other versions of fast RLS algorithms that have a computational complexity of IN have been given in the literature [4], [5], but these algorithms are considerably more sensitive to round-off noise, especially in fixed-point implementations. Much work has been done toward the understanding of the numerical stability of this class of algorithms and some methods have been devised to improve their numerical stability [6]. The linear equalizer based on the RLS criterion may also be

- 35B -

TABLE HI RLS LATTICE-LADDER ALGORITHM

Lattice Predictor: Begin with / = 0 and compute the order updates for m = 0, \,-",N - 2 l)f _{m }(t)b*(t - 1)

/« i> _{m } l)

^ _{+ }.(0 = r°(t- 1)- l*« _{+ }ι(

^( «« _{+ }ι(0 = « ( -

Ladder Filter: Begin with t = 0 and compute the order updates for m = 0, 1,-", N - 1

<f _{m }(t) = wd t - 1) + α _{m }(t)6*(t)e _{m }(t) (t)= -^

«m _{+ }ι(' + i) = *„,(' + l) + Ϊ Ob t + l)

Initialization y(t + 1)

implemented as a lattice structure [2], [7]. This structure is illustrated in Fig.4, and the corresponding algorithm is summa¬ rized in Table HI. It has a computational complexity of 13/V complex multiplications and divisions. This linear growth in complexity makes this lattice equalizer very attractive in practi¬ cal applications where large equalizer lengths are required to cope with large channel dispersion.

- 36 -

- 36A -

From the observation of the structure of the equalizer shown in Fig. 4, we note that it consists of two parts, a lattice filter and a ladder filter. The ladder section is sometimes called a "joint process estimator." It is that part of the equalizer that forms a weighted linear combination of the so-called backward residuals {b _{m }(t)} to yield the equalizer output.

We should emphasize that the RLS lattice-ladder structure for the linear FIR equalizer shown in Fig. 4 is mathematically equivalent to the RLS transversal equalizer structure. Hence the performance of these two RLS equalization algorithms is identi¬ cal provided that the computations are performed with infinite precision. However, the numerical properties of these structures and their corresponding algorithms are different when fixed-point arithmetic is used [2], [8].

The RLS lattice-ladder algorithm given in Table III is by no means unique. Modifications can be made to some of the equa¬ tions without affecting the optimality of the algorithm. However, some modifications result in algorithms that are more robust numerically when fixed-point arithmetic is used in the implemen¬ tation of the algorithm. Of particular interest is the modification in the manner in which the reflection coefficient j,(t) and Jt' _{m } it) in the lattice and the gains ξ _{m }( in the ladder are computed. Instead of the conventional method given in Table in, these parameters may be time-updated directly, according to the equations [2], [9]:

*f (,) - *' ,, _ * _ !__L__}_________A

(7) c t - \) f*(t) b _{m } , At) x _{m }\M = * .(' - l) - -=i >' ^{m }, ) ' ^{m÷Λ > } (8)

( ' )

An important characteristic of these direct time-update equations

- 36B -

TABLE IV GRADIENT LATTICE-LADDER ALGORITHM υ _{m }(t) = wυ _{m }(t - 1) + | / _{M }_ ,<0 | ^{2 } + \ b _{m }_ ,(t - D | ^{2 } k _{m }{t) = k _{m }(t - 1)

/„,- ,(' - !) -%(* ~ 1) + -fta- iQ ~ 2)/ _{m }(t - 1)

- l) )

£

Initialization

/o(0 = V = O / _{M }(- 1) = - 1) = -2) = 0 e _{0 }(t) = /(/) e _{m }(0) = 0 m > 1 υ _{m }(- l) = e > 0

S«<0) = 0 * _{m }(- l) = 0

is that the forward and backward residuals {/ _{m }( } and { b _{m }(f)} are fed back to time-update the reflection coefficients in the lattice stages, and e _{m + } ,(t) is fed back to update the ladder gain. The resulting RLS lattice-ladder algorithm is called the "error- feedback RLS algorithm" and has been shown to be significantly more robust to round-off errors than the conventional form [9].

A computationally simpler algorithm, albeit slower converg¬ ing than the RLS algorithm, for the lattice-ladder structure is the gradient lattice-ladder algorithm. The structure is illustrated in Fig. 5 and the corresponding algorithm is given in Table IV. Fig. 6, due to Satorius and Pack [7], illustrates the initial convergence of this algorithm as compared to the convergence of the RLS lattice-ladder algorithm and the LMS (gradient) algorithms for a transversal equalizer of length, N = 11. Note that the gradient-lattice algorithm is only slightly slower than the RLS lattice algorithm, but significantly faster than the LMS algorithm.

Both the linear transversal and lattice equalizers are all-zero

- 37 -

Fig. 6. Comparison of convergence rate of RLS lattice, gradient lattice, and LMS (gradient) algorithms.

(FIR) filters. The implementation of a linear equalizer as an infinite duration impulse response (IIR) filter structure (direct form or lattice) can be easily accomplished by adding a filter section that contains poles. However, the addition of poles in an adaptive filter entails the risk that one or more poles may move outside the unit circle during adaptation and render the equalizer unstable. Usually, the risk of instability far outweighs the small benefits in reduced complexity (fewer filter coefficients) that the IIR filter may yield [2, chap. 6]. Consequently, adaptive IIR equalizers are seldom used in practice.

Linear equalizers find use in applications where the channel distortion is not too severe. In particular, the linear equalizer does not perform well on channels with spectral nulls in their frequency response characteristics. In an attempt to compensate for the channel distortion, the linear equalizer places a large gain in the vicinity of the spectral null and, as a consequence, significantly enhances the additive noise present in the received signal. Such is the case in many fading channels. Consequently, use of linear equalization should be avoided under such channel conditions. Instead, one of the nonlinear equalization methods described below may be used.

- 37A -

B. Nonlinear Equalizers

Nonlinear equalizers are used in applications where the chan¬ nel distortion is too severe for a linear equalizer. We emphasize that the channel distortion causing the ISI is linear, but the signal-processing operations performed on the signal are nonlin¬ ear.

Three very effective equalization methods have been devel¬ oped over the past two decades. One is decision feedback equalization. The second is a symbol-by-symbol detection algo¬ rithm based on the maximum a posteriori probability (MAP) criterion proposed by Abend and Fritchman [10]. The third is a sequence-detection algorithm, based on the maximum-likelihood sequence estimation (MLSE) criterion, which is efficiently im¬ plemented by means of the Viterbi algorithm (VA) [11]. We briefly describe the key features of these equalization methods.

1) Decision-Feedback Equalizer (DFE): The basic idea in DFE is that once an information symbol has been detected, the ISI that it causes on future symbols may be estimated and subtracted out prior to symbol detection. The DFE may be realized either in the direct form or as a lattice. The direct-form structure of the DFE is illustrated in Fig. 7. It consists of a feed-forward filter (FFF) and a feed-back filter (FBF). The latter is driven by decisions from the output of the detector, and its coefficients are adjusted to cancel the ISI on the current symbol that results from past detected symbols (postcursors). The coef¬ ficient adjustment may be performed as in the linear equalizer by the relatively simple gradient LMS algorithm, as shown in Fig. 7, or by the faster converging RLS algorithm; e.g. , the square- root RLS or the fast RLS algorithm which are given in [13] and [14].

- 37B -

An alternative form of the DFE is the RLS lattice structure that is illustrated in Fig. 8. This structure is equivalent to a direct form (transversal-type) DFE having a FFF of length N, , and a FBF of length N _{2 } , where we assume that N, ≥ N _{2 } • In the lattice structure shown in Fig. 8 we note that the lattice stages are of two types, single channel and two-channel lattices. There are N _{x }-N _{2 } single-channel lattice stages, which have basically the same form as the lattice stages in a linear FIR lattice filter, and one transitional stage. There are also N _{2 } — 1 two-channel lattice stages whose input and output consists of two two-dimen¬ sional vectors, and the lattice-gain factors (the reflection coeffi¬ cients) are also two-dimensional vector quantities. The order update and time-update equations for the lattice DFE are given in Table V. The ladder part (the joint-process estimator) which forms estimates of the information symbols is similar in form to the ladder section in the linear RLS lattice-ladder equalizer.

A gradient lattice DFE can be obtained from the RLS lattice DFE by making a minor modification to the update equations given in Table V. In particular, if we set a _{m }{t) equal to unity and eliminate the update equations for ct _{m }(t), the RLS lattice DFE degenerates into the gradient lattice DFE. Thus we obtain a computationally simpler algorithm at the expense of a small degradation in the convergence rate.

Another form of a DFE, proposed by Belfiore and Park [15], is called a " predictive DFE. " The basic structure for the predictive DFE is illustrated in Fig. 9. It also consists of a FFF as in the conventional DFE. However, the FBF in the predictive DFE is driven by an input sequence formed by the difference of the output of the detector and the output of the FFF. (In the conventional DFE, the input to the FBF is the output of the detector.) As a consequence, the FBF is called a noise predictor, because it forms an estimate (or a prediction) of the noise and residual ISI contained in the signal at the output of the FFF and subtracts from it the detector output after some feedback delay. It can be shown [2], [15] that the predictive DFE performs as well as the conventional DFE in the limit as the number of taps in the FFF and FBF approach infinity. However, for a finite-

- 37C -

length equalizer the conventional DFE structure performs better than the predictive DFE structure. One important advantage of the predictive DFE is that it can be used as an equalizer for trellis-coded modulated signals, which are decoded by use of the Viterbi algorithm [16], [17].

The FFF of the predictive DFE may also be realized as a lattice structure as demonstrated by Zhou et al. [16]. Thus the RLS lattice algorithm may be used in the FFF to yield fast convergence, if necessary. The FBF may be implemented either as a direct-form (transversal) FIR filter structure or as a lattice structure, and either the gradient LMS or an RLS algorithm may be used to adapt the filter weights, depending on the speed of convergence required to track the channel variations.

In general, the class of RLS algorithms provide faster conver¬ gence to changes in time-variant channel characteristics than the LMS algorithm. The convergence rate of the LMS algorithm is especially slow in channels which contain spectral nulls, whereas the convergence rate of the RLS algorithm is unaffected by the channel characteristics.

- 38 -

- 38A -

- 38B -

The price to be paid for faster convergence is an increase in computational complexity. Fig. 10 illustrates the computational complexity of the LMS and RLS DFE algorithms. We observe that the LMS algorithm is by far the simplest to implement. Its computational complexity is proportional to 2N, where N is the total (FFF and FBF) equalizer length. The fast RLS algorithm for a transversal structure equalizer is the most computationally efficient among the RLS algorithms. Its computational complex¬ ity is approximately proportional to 20 N. The gradient lattice algorithm, which is a computationally simpler version of the

RLS algorithm, albeit suboptimum in terms of rate of conver¬ gence, also has a computational complexity proportional to N, but the proportionality constant is smaller than that for the RLS lattice algorithm. Finally, the square-root RLS algorithm has a computational complexity proportional to N ^{2 }, which renders the algorithm computationally inefficient for large equalizer lengths, as can be observed from Fig. 10. Table VI summarizes the computational complexities of the various DFE algorithms. In this table, N, denotes the number of coefficients in the FFF, N _{2 } denotes the number of coefficients in the FBF, and N = /V, -

- 39 -

TABLE V RLS LATTICE DFE ALGORITHM

Initialization

WO = Mt) = y(t), k O) = 0 (M = N, - N _{2 }) ) = r»{t) = wrfrt - 1) + | j</) | ^{2 }, e _{0 }(t) = x(t), oO = 0 _{m }(t) = 1, k _{m }* ) = 0, r (0) = r (0) = δ

(m= 1,---,N, -N _{2 }- 1) k O) = *i(0) = 0, * _{m }(0) = 0, Ar (0) = 0 ri ) = r£(0) = hi ( = N, - N _{2 },- • ^{• }, N _{x }).

Scalar Lattice Stages (0 < m < N, — N _{2 } unless other-wise specified)

Transitional Lattice Stage (M = N _{x } — N _{2 }) it) = e _{M } ,{t - 1) - k _{M } ^{b }(t - l)Λ,_ _{. }(t)/r _,(t - 1) *ir( = »•*&( - 12) + _{M }_ _{x }(t - l)/j&_,(/ - D ^.^t - 1)

Λ _{/ }(0 = [Λ _{f }( , ^{β } _{w }(/ - l)]'

W) = πτ (t - 1) + «„(/ - 1)/A,(0/J&<0

*i ^{( } = »W - i ^{) } + ^{β }A ^{( } *& ^{( } .

Two-Dimensional Lattice Stages (N — N _{2 } < m < N _{x } unless

- 39A -

N _{2 }. The graphs shown in Fig. 10 are based on the assumption that N _{x } = N _{2 } = N/2.

2) Probabilistic Detection Algorithms: The MAP algorithm and MLSE algorithm are optimal in the sense that they minimize the probability of error. In the MAP algorithm, it is the symbol error rate that is minimized. In MLSE, the Viterbi algorithm minimizes the probability of a sequence error. In practice, these two probabilistic-detection algorithms provide comparable per¬ formance. A description of the algorithms and their performance characteristics are given in [10], [11], [2].

The symbol-by-symbol MAP and the MLSE algorithms re¬ quire knowledge of the channel characteristics in order to com¬ pute the metrics (probabilities) for making decisions. In the absence of such knowledge, the channel must be estimated. Channel estimation can be accomplished adaptively, as illus¬ trated in Fig. 11. The channel estimator is usually an FIR transversal filter with adjustable coefficients. Either the gradient LMS algorithm or one of the class of the faster converging RLS algorithms may be used to adjust the coefficients of the channel estimator. These estimated coefficients are fed to the probabilis¬ tic symbol-by-symbol MAP algorithm or the MLSE-based Viterbi algorithm for use in the metric computations.

In addition to knowledge of the channel characteristics, the MAP and MLSE algorithms also require knowledge of the statistical distribution of the noise corrupting the signal. Thus the probability distribution of the additive noise determines the form of the metric for optimum demodulation of the received signal.

For time-dispersive channels in which the ISI spans many

- 39B -

Fig. 9. Block diagram of predictive DFE.

Total number of taps

Fig. 10. Computational complexity of DFE algorithms.

- 39C -

TABLE VI COMPUTATIONAL COMPLEXITY OF ADAPTIVE DFE ALGORITHMS

Total number of Number of

Algorithm complex operations divisions

symbols, these probabilistic algorithms become impractical due to an exponentially growing computational complexity with ISI span. Nevertheless, they serve as benchmarks against which we can compare the performance of suboptimal algorithms such as the DFE and the linear equalizer.

C. Symbol Versus Fractionally Spaced Equalizers

It is well known [2] that the optimum receiver for a digital communication signal corrupted by additive white Gaussian noise consists of a matched filter that is sampled periodically at the symbol rate. If the received signal samples are corrupted by

- 40 -

(a)

Fig. 11. (a) Probabilistic symbol detection with adaptive channel estima¬ tion, (b) Adaptive channel estimation.

SUBSTITUTE SHEET {RULE 26)

40A

intersymbol interference, the symbol-spaced samples are further processed by either a linear or nonlinear equalizer.

In the presence of channel distortion, the matched filter prior to the equalizer must be matched to the channel-corrupted signal. However, in practice the channel impulse response is usually unknown and, consequently, the optimum matched filter to the received signal must be adaptively estimated. A subopti- mum solution in which the matched filter is matched to the transmitted signal pulse may result in a significant degradation in performance. In addition, such a suboptimum filter is extremely sensitive to any timing error in the sampling of its output [18].

A fractionally spaced equalizer (FSE) is based on sampling the incoming signal at least as fast as the Nyquist rate. For example, if the transmitted signal consists of pulses having a raised cosine spectrum with roll-off factor β, its spectrum ex¬ tends to F _{max } = (1 + β)/2 T. This signal may be sampled at the receiver at the minimum rate of

1 + β 2F _{mzx } = —-- ( 10)

and then passed through an equalizer with a tap spacing of 7/(1 4- β). For example, if β = 1 , we require a T/2-spaced equalizer. If β = 1 /2, we may use a 27 ^{" }/3-spaced equalizer, and so forth. In general, a digitally implemented, fractionally spaced equalizer has tap spacings of KT/L, where K and L are integers and K < L. Often, a T/2-spaced equalizer is used in many applications, even in cases where a larger tap spacing is possible. The frequency response of a FSE is [2]

C (/) = ^{N }± c _{k }e- *' ^{kr } (11)

A: =0 where 7" = KT/L. Hence C _{r }(/) can equalize the received

- 40B -

signal spectrum beyond the Nyquist frequency up to / = L j KT. The equalized spectrum is

(12) where X(f) is the input analog signal spectrum, Y _{τ }.(f) is the spectrum of the sampled signal, and τ _{0 } is a timing delay. Since X(f) = 0 for I / I > L i ' KT, the above expression reduces to

cΛf) YAf) = c _{r }{f) x(/)ew , \f \ ≤ ~.

(13)

Thus the FSE compensates for the channel distortion in the received signal before aliasing effects occur due to the symbol rate sampling. In addition, the equalizer with transfer function CY _{' }( ) ^{can } compensate for any timing delay τ _{0 }; i.e., for any arbitrary timing phase. In effect, the fractionally spaced equal¬ izer incorporates the functions of matched filtering and equaliza¬ tion into a single-filter structure.

The FSE output is sampled at the symbol rate 1 / T and has a spectrum:

Its tap coefficients may be adaptively adjusted once per symbol as in a T-spaced equalizer. There is no improvement in the convergence rate by making adjustments at the input sampling rate of the FSE.

- 40C -

Simulation results demonstrating the effectiveness of the FSE over a symbol-rate equalizer have been given in the papers by Qureshi and Forney [18] and Gitlin and Weinstein [19]. We cite one example from the first paper. Fig. 12 illustrates the perfor¬ mance of the symbol rate equalizer and 7/2-spaced equalizer for a channel with high-frequency amplitude distortion, whose characteristics are also shown in this figure. In this example, the symbol-spaced equalizer was preceded by a filter matched to the transmitted pulse that had a (square-root) raised cosine spectrum with a 20% roll-off factor { β = 0.2). The FSE did not have any filter preceding it. The symbol rate was 2400 Bd and the modulation was QAM. The received SNR was 30 dB. Both equalizers had 31 taps; hence the 7/2 FSE spanned one-half of the time interval of the symbol-rate equalizer. Nevertheless, the FSE outperformed the symbol-rate equalizer even when the latter was optimized at the best sampling time. Furthermore, the FSE did not exhibit any sensitivity to the timing phase as shown in Fig. 12. Similar results were later obtained by Gitlin and Weinstein [19].

The above results clearly demonstrate the advantages of FSE's over symbol rate equalizers. FSE's are currently in use in nearly all commercially available high-speed modems over voice- frequency channels.

In the implementation of the DFE, the FFF should be frac¬ tionally spaced, e.g. , 7/2-spaced taps, where 1 / 7 is the sym¬ bol rate, and its length should span the total anticipated channel dispersion. The FBF has 7-spaced taps, and its length should also span the anticipated channel dispersion.

- 41 -

Frequency ( Hz) (a)

Time, symbol intervals

(b) Fig. 12. 7 and 7/2 equalizer performance as a function of timing phase for 2400 symbols per second, (a) Channel with high-end amplitude distortion (HA), (b) Equalizer performance. (Reference [18]. © 1977 IEEE, reprinted with permission.)

- 41A -

III. CHARACTERISTICS OF UNDERWATER ACOUSTIC

TELEMETRY CHANNELS AND THEIR IMPACT ON

ADAPTIVE EQUALIZATION

Underwater acoustic channels are generally characterized as fading multipath channels. The multipath is quite variable and depends on a variety of factors, including ocean depth and the propagation path length. Channel-time variations are also quite variable and depend on a variety of sea conditions, including the sea state and depth.

Short-range (below 1 km) acoustic telemetry channels that transmit in the 10-50 kHz frequency range are particularly suitable for adaptive equalization. Such channels include vertical deep-water communication links [20] -[23] and short-range hori¬ zontal communication links [24], [25]. The received signal usually consists of a direct path, surface reflections, and, occa¬ sionally, bottom-induced multipath. In such channels, the signal amplitude and phase fluctuations are relatively mild, and the direct pat serves as a stable reference from which time synchro¬ nization can be acquired.

Medium-range (1 -20 km) horizontal-path acoustic telemetry channels exhibit more severe signal amplitude and phase fluctu¬ ations. Doppler spreads in the range of 50 Hz are frequently observed, and the multipath spread may be of the order of 50 ms to as much as a second. In shallow water, both surface- and bottom-propagation paths are usually observed [26] -[28]. Such channels are particularly difficult to equalize in both amplitude and phase. In fact, most of the acoustic telemetry systems currently in use on such channels employ multitone frequency- shift keying (FSK) and noncoherent (energy-type) detection at the receiver [28] -[31]. Since single-carrier coherent phase-shift keying (PSK) provides greater bandwidth efficiency and, hence, a higher data rate in b/Hz, more effort should be devoted to investigating the performance capabilities and limitations of adaptive equalizers for such channels. In particular, the block- processing equalization methods described in the following sec¬ tion appear to be the most promising.

- 41B -

Of particular importance in any investigation of adaptive equalization for fading multipath channels is the frequency selec¬ tivity, due to time- varying multipath, which results in spectral nulls in the channel frequency response. In such channel condi¬ tions, linear equalizers perform poorly and should be avoided. Only the nonlinear equalization methods (DFE, MAP, and MLSE) are able to cope with spectral nulls in the channel response.

Long-range (20-2000 km) telemetry systems typically operate in the frequency range below 10 kHz in order to overcome the high transmission loss. In such long propagation ranges the received signal paths exhibit good phase stability and, hence, phase-coherent modulation and demodulation is possible [32].

The characteristics of the ambient noise [27], [30] are another important consideration in the design of an adaptive equalizer for acoustic telemetry. The optimum MAP and MLSE algo¬ rithms require knowledge of the noise statistics for metric com¬ putations. Typically, the presence of Gaussian noise is assumed. However, the ambient noise below 10 kHz is non-Gaussian. As a consequence, the MAP and MLSE algorithms implemented on the basis of a Gaussian noise assumption may not perform as well as a DFE, which makes no assumptions about the statistical properties of the noise. In other words, the DFE is generally more robust than the MAP and MLSE algorithms in the absence of knowledge of the statistical properties of the ambient noise. On the other hand, as the frequency is increased above 10 kHz, the ambient-noise level decreases and tends toward Gaussian. In such a case, the MAP and MLSE algorithms will outperform the DFE.

- 41C -

IV. SEQUENTIAL VERSUS BLOCK PROCESSING EQUALIZATION ALGORITHMS FOR ACOUSTIC TELEMETRY

CHANNELS

The adaptive equalization methods described in Section II, process the received information symbols sequentially. In a fading channel environment, we must be concerned with time intervals in which the received signal fades to nearly the level of the background noise and the corresponding error rate becomes very high; e.g. , 10 ^{" } ' or higher. In such a case, the decisions from the detector are not sufficiently reliable to be used in a decision-directed mode for self-adaptation. When the signal comes out of the fade and begins to increase, the equalizer is hampered by these unreliable decisions and takes a significant amount of time to converge to the new channel conditions. Much faster convergence can be obtained if the transmitter in informed of the poor channel conditions during periods of severe signal fading and switches into the transmission of a training sequence until such time when the signal level exceeds a given threshold. This type of adaptive operation requires a feedback link from the receiver to the transmitter, which is used by the receiver to inform the transmitter when severe signal fading occurs. When no feedback link exists, the transmitter may transmit training

detection block f^ known Md unknown fi known training symbols data symbols raining symbols

L training block —→ data block

Fig. 13. Format for block processing equalization.

- 42 -

symbols imbedded in the information sequence. Thus, when the signal fades, only the training symbols are used in equalizer adaptation.

An alternative to sequential processing for recovery of the information symbols is block processing, where each block contains a sequence of training symbols and a sequence of data symbols. The training symbols in each block are used to esti¬ mate the channel impulse (or frequency) response, and the channel estimate is used in the detection of the data symbols. Such an approach has been investigated by Hsu [33], Davidson et al. [34], and Crozier [35], [36]. In these schemes a typical block consists of M _{t } training symbols followed by a block of M _{d } data symbols, as shown in Fig. 13. The two blocks of training symbols on either side of the block of data symbols may be used for channel estimation and data detection. The block sizes are selected to be sufficiently short to render the channel time-invariant for the duration of the two blocks' M _{t } and M _{d } symbols.

Hsu [33] investigated a nonlinear decision-feedback symbol detection technique in which the training symbol blocks on each side of a data block are used for channel estimation. Then a DFE-type detection algorithm is employed to make decisions on the first and last symbols in the data block, say, b _{x } and b _{M x }. These detected symbols are treated as additional training sym¬ bols to estimate the channel response again and, then, to use the new channel estimate in the detection of the next _two outermost symbols, b _{2 } and b _{Md }_ _{2 }. The detected symbols b _{2 } and b _{Md }_ _{2 } are again treated as additional training symbols, and the estima¬ tion/detection procedure is repeated until all data symbols in the block are detected. In essence, this detection technique is a block DFE, where a pair of data symbols is detected recursively in each iteration.

- 42A -

Crozier [35], [36] also investigated a block-detection tech¬ nique in which the training-symbol blocks on both sides of the data-symbol block are used in the estimation of the channel and detection of the data symbols. The least-squares error criterion was employed in the design of a linear estimator, a decision- feedback estimator, and a maximum-likelihood estimator of the block of symbols. The detection method for the decision-feed¬ back block estimation was basically the recursive scheme pro¬ posed by Hsu [33].

Davidson et al. [34] compared the computational complexity of a block-adaptive DFE with a square-root RLS DFE and illustrated that the computational complexity of the block adap¬ tive DFE is significantly less than the square-root RLS for equalizer lengths of 10 or more.

An important consideration in the design of the adaptation scheme is channel fading, and the corresponding coherence time (reciprocal of the Doppler spread) of the channel. In particular, when the coherence time is small relative to the block length, a channel measurement made at the beginning of a block from the training symbols may be inadequate for reliably detecting sym¬ bols that occur later in the block. In such a case, the block-adap¬ tive DFE scheme of Hsu [33], which augments the channel measurement by the inclusion of data symbols that have been detected, should prove very effective. Other schemes based on block adaptation with channel tracking via interpolation between successive blocks of training symbols have been proposed by Davidson et al. [34] and Lo et al. [37]. At the present time there is insufficient data on the performance of these block processing schemes under various channel conditions to make a decision as to which method is most appropriate for underwater acoustic telemetry channels. Investigations are currently in progress to evaluate the performance capabilities of block- processing adaptive equalization methods for use in underwater acoustic telemetry.

- 42B -

V. CONCLUDING REMARKS

We have provided a survey of linear and nonlinear adaptive equalization techniques for combating intersymbol interference in digital communications over time-dispersive channels. Vari¬ ous equalizer structures and associated adaptive algorithms were considered, including both fractionally spaced and symbol-spaced equalizers.

Adaptive equalization techniques may be applied to acoustic telemetry channels to achieve high data rates in cases where the signal amplitude and phase fluctuations are sufficiently slow to allow for channel estimation and tracking. Either sequential RLS or block-processing equalization algorithms are suitable for slowly fluctuating channels. The block-processing algorithms appear to be particularly attractive for acoustic telemetry chan¬ nels with more severe channel variation, such as those encoun¬ tered in medium-range shallow-water links. Due to spectral nulls that occur from fading multipath, only nonlinear equalization techniques are appropriate for acoustic telemetry.

Investigations on the performance of block-processing adap¬ tive equalization algorithms are currently in progress. The re¬ sults of these investigations will form a basis for future acoustic communication systems which will employ adaptive equalization to combat ISI.

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1978. [32] T. Birdsall. "Acoustic telemetry for ocean acoustic tomography,"

/£E£ J. Oceanic Eng., vol OΕ-9, pp. 237-241 , Oct. 1984. [33] F. Hsu, "Data-directed estimation techniques for single-tone HF mode s," in Proc. MILCOM '85 (Boston, MA),~Oct. 1985, pp. 12.4.1 - 12.4.10. [34] G. W. Davidson, D. D. Falconer, and A. U. H. Sheikh, "An investigation of block-adaptive decision feedback equalization for frequency selective fading channels," Can. J. Elec. Comp.

Eng., vol. 13, nos. 3/4, pp. 106- 1 11 , Mar. 1988. [35] S. N. Crozier, D. D. Falconer, and S. Mahmoud, "Short-block equalization techniques employing channel estimation for fading time-dispersive channels," in Proc. IEEE Vehicular Tech.

Conf. (San Francisco, CA), May 1989, pp. 142- 146. [36] S. N. Crozier, "Short-block data detection techniques employing channel estimation for fading, time-dispersive channels," Ph.D. thesis, Dept. Syst. Computer Eng., Carleton Univ., Ottawa, ON,

Can. , Apr. 1990. [37] N. K. W. Lo, D. D. Falconer, and A. U. H. Sheikh, "Adaptive equalization and diversity combining for a mobile radio channel," presented at Globecom '90. San Diego, CA, Dec. 1990. [38] G. J. Bierman, Factorization Methods for Discrete Sequential

Estimation. New York: Academic, 1977.

John G. Proakis (S'58-M-62-SM'82-F'84) received the E.E. degree from the University of Cincinnati in 1959, the S.M. degree in electrical engineering from the Massachusetts Institute of Technology, Cambridge, in 1961 , and the Ph.D. degree in engineering from Harvard University, Cambridge, in 1966.

From June 1959 to September 1963 he was associated with MIT, first as a Research Assis¬ tant and later as a Staff Member at the Lincoln Laboratory, Lexington, MA. During the period

- 43C -

1963- 1966 he was engaged in graduate studies at Harvard University, where he was a Research Assistant in the Division of Engineering and Applied Physics. In December 1966 he joined the Staff of the Communi¬ cation Systems Laboratories of Sylvania Electronic Systems, and later transferred to the Waltham Research Center of General Telephone and Electronics Laboratories, Inc., Waltham, MA. Since September 1969 he has been with Northeastern University, Boston, MA, where he holds the rank of Professor of Electrical Engineering. From July 1982 to June 1984 he held the position of Associate Dean of the College of Engineer¬ ing and Director of the Graduate School of Engineering. Since July 1984 he has been Chairman of the Department of Electrical and Computer Engineering. His interests have centered on digital communi¬ cations, spread spectrum systems, system modeling and simulation, adaptive filtering, and digital signal processing. He is the author of the book, Digital Communication (New York: McGraw-Hill, 1983, 1989, second edition), and the coauthor of the book. Introduction to Digital Signal Processing (New York: Macmillan, 1988).

Dr. Proakis has served as an Associate Editor for the IEEE TRANSAC¬ TIONS ON INFORMATION THEORY (1974- 1977), and the IEEE TRANSAC¬ TIONS ON COMMUNICATIONS (1973- 1974). He has also served on the Board of Governors of the Information Theory Group (1977- 1983), is a Past Chairman of the Boston Chapter of the Information Theory Group, is a Registered Professional Engineer of the State of Ohio, and is a member of Eta Kappa Nu, Tau Beta Pi, and Sigma Xi.

- 44 -

%config.m APPENDIX B

Ns=12; % samples per symbol

N=2*2*2; % feedforward taps

FS=2;NN=N/FS; % fract. spacing and numb, of ff symbols

Nplus=NN/2;

M=2;

Q=i;

K=l; % number of channels delta=0.001;P=eye(N*K+M) /delta;L=0.99;

Nt=43+225;

Nd=43+5*255; % (255,511,2047,4095) dseqfile='dseq33 ' ;

%Ka=0.03;Kb=0.03; a=zeros (1,N*K) ;b=zeros(1,M) ;c=[a -b] ;

Kf1=0.03 ;Kf2=Kfl/10;Lf=l;

%Ktl=0.07;Kt2=Ktl/10;Lt=l; load qps 33_dl2_80nm_ch9_inp;

if K~=l;

vl=v;

load qpsk33_dl2_80nm_chl_inp; v2=v;

%load qpsk33_dl2_80nm_ch6_inp; %v3=v;

len=min ([length(vl) length(v2) ]) ;

vl=vl ( 1 : len) ; v2=v2 ( 1 : len) ;

- 45 -

%v3=v3 (l:len) ;

v=[vl;v2]; clear vl v2; end;

eval (['load 'dseqfile]; dseq=eval(dseqfile) ; pn=dseq(44:length(dseq) ) ; d=[dseq pn pn pn pn] ; clear dseq pn; d=d(l:Nt) ;

% jointfsrls.m

Initialization

f(l)=0 phase

%a=zeros (1,N) ; feedforward equalizer taps %b=zeros (1,M) ; feedback equalizer taps c=[a -b] ; x=zeros (1,N) ; input signal vector

(in ff section)

Sf=0; PLL integrator output dd=zeros (1,M) ; vector of previous decisions

(in fb section) sse=0; sum of squared errors

%C=zeros (Nd,N+M) ; I matrix of equalizer taps in time

%P=eye(N+M) /delta; inverse correlation.matrix for RLS

for n=l:Nd; n

%%%%read new sample%%%%

- 46 -

nb=(n-l) *NS+(Npluε-l) *Ns % current input sample xn=[];for 1=1:FS; xn=[v(nb+(2*1-1) *Ns/2/FS)xn] ; end;

FS new input samples x=[xn x] ; x=x(l:N);

%%%%compute new signalε%%%

p=x*a'*exp(-j*f(n) ) ; % output of ff section with corrected phase z(n)=p; q=dd*b' ; % output of fb section de(n)=p-q; % estimate of data d(n) if n>Nt % Nt=training length; % d(n)=real (decision(d(n) )) ; % BPSK d(n)=decision(de(n) ) ; % QPSK % d(n)=decision8 (de(n) ) ; % 8-QAM % d(n)=decision8psk(de(n) ) ; % 8-PSK end; e=d(n) -de(n) ; % error et(n)=e; sse=sse+abs (e ^{Λ }2) ; mse(n)=sse/n; mse(n)

%%%%parameter update%%%%

y=[x*exp(-j*f(n) ) dd] ; % data vector for RLS

Sf=Lf*Sf* imag(p*conj (d(n)+q) ) ; % PLL f (n+l)=f (n)+Kfl*imag(p*conj (d(n)+q) )+Kf2*Sf;

k=P/L*conj (y') / (1+conj (y)*P/L*conj (y') ) ; % RLS c*=c+conj (k' ) *conj (e) ; P=P/L-k*conj (y) *P/L;

a-c(l:N) ;b=-c(N+l:N+ M) ; dd=[d(n) dd]; dd=dd(l:M);

- 47 -

% C (n , : ) = [ a -b] ;

end ;

function p=preamb4psk(nconst,nch,nalt, init, ult)

% premamb(nconst,nch, init) synthesizes a preamble for phase modulation. % the first nconst symbols are equal to init.

Then follow nch symbols % calculated as P(i)=p(i-l) *mult. The preamble is ended by nalt symbols % calculated as p(i)=-p(i-l) . p=init. *ones(1,nconst) ; dat=init; for i=l:nch, dat=dat*mult; p(nconst- i)=dat; end for i=l:nalt, dat=-dat; p(nconst+nch+i)=dat; end

%script file to demodulate qpsk 333 baud transmission load csblock240-260.mat qpsk = aOP(250000:400000) ; clear aOP freq_data = fft (qpsk,2 ^{Λ }18) ; clear qpsk len = length (freq_data) ; freq_data ( (len/2+1) : len = zeros (1, len/2) ; shift_data (l:len/4) = freq_data (len/4+1: len/2) ; shift_data (3*len/4+l: len) = freq_data (l:len/4); clear freq_data pack

- 48 -

%filt = remez (255, [0 0.15 0.2 1], [1 1 0 0], [1 100]);

%600 Hz bandwidth (+-300) in load filt 333 qpsk = ifft (shift_data.*conj (fft(filt,2 ^{Λ }18) ) ) ;

qpsk333 = qpsk(l: 150000) ;

save temp qpsk333

- 49 -

An Algorithm for Multichannel Coherent Digital Communications Over Long Range Underwater Acoustic Telemetry Channels

M. Stojanovic, J. Catipovic" and J.G. Proakis Dept.of Electrical and Computer Engineering "Woods Hole Oceanographic Institution

Northeastern University Woods Hole, MA 02543

Boston, MA 02115

Abstract - The problem of achieving reliable digi¬ tal communications over long range underwater acoustic telemetry channels is addressed, and a receiver algorithm for multichannel coherent data detection is presented. The receiver consists of a T/2 fractionally spaced bank of feedforward equalizers, a multichannel carrier phase syn¬ chronizer and a common decision feedback section of the equalizer. An adaptive algorithm is derived based on joint minimum mean squared error optimization of the receiver parameters. The equalizer tap coefficients and estimates of the carrier phases are updated using a combination of a recursive least squares algorithm and a second order mul¬ tichannel digital phase locked loop. Since the equalizer accomplishes the function of symbol synchronization, no separate delay locked loops are necessary.

The algorithm is successfully applied to the experi¬ mental data. The results assert feasibility of coherently combining multiple arrivals in each of the diversity chan¬ nels, and demonstrate additional spatial diversity im¬ provement.

- 49A -

I. INTRODUCTION

Although the underwater acoustic (UWA) channel fits into the general description of a rapidly fading channel, many of the classical communication techniques, such as those designed for the VHF/UHF mobile radio channels, are not directly applicable to the UWA channel due to its many unique characteristics. Severe performance degra¬ dation encounterd on the UWA channels is largely due to the extended, time varying multipath and phase in¬ stabilities, the latter of particular concern for long range telemetry [1]. While typical multipath spreads in the mo¬ bile radio channel are two or three symbol intervals, in the long range UWA channel they increase to several tens of symbol intervals for moderate to high data rates. On the other hand, a receiver capable of coherently processing multiple arrivals benefits from both power efficiency of coherent detection and diversity improvement inherent in multipath propagation. Due to the rapid fluctuations of the ocean channel, such a receiver is likely to be compu- tationaly intensive, and is often not considered feasible. Fortunately enough, the computational complexity is not of a major concern in the UWA communications, since the data rates are considerably lower than those used in the majority of existing communication media.

In order to account for both amplitude and phase fluc¬ tuations of the UWA channel, we address the problem of jointly adaptive synchronization and channel equaliza¬ tion. Joint estimation procedures are known to yield bet¬ ter results than marginal estimation, and the fundamen¬ tal work in this area was presented in [2], [3]. Since both of these references concentrate on the optimal, maximum likelihood sequence estimation principles, which become inacceptably complex for long channel responses spanning more than, say, ten symbol intervals, we focus on a subop- timal receiver structure with a decision feedback equalizer (DFE). The concept of joint carrier and symbol synchro¬ nization, and DFE [4] is extended here to multichannel,

- 49B - or spatial diversity reception, which provides additional improvement in performance with respect to fading and noise. To meet the rapidly changing conditions in the channel, the receiver operates using a combination of re¬ cursive least squares (RLS) algorithm for equalizer coef¬ ficients update, and a second order multichannel digital phase locked loop (DPLL) for carrier phase synchroniza¬ tion. The receiver requires only two samples per symbol interval, and is suitable for an all digital implementation. After considering the general receiver structure in Sec¬ tion 2, the derivation of the receiver algorithm is given in Section 3. Section 4 presents some of the results ob¬ tained with the experimental long range UWA telemetry data provided by the Woods Hole Oceanographic Institu¬ tion (WHOI).

II. COMMUNICATION SYSTEM STRUCTURE

We consider a general class of linear, bandwidth effi¬ cient modulation techniques. The transmitted signal is represented in its equivalent complex baseband form as

u(t) = ^{d }( ^{n })9(t - nT) (1)

- 50 -

Figure 1: Signaling frame.

Figure 2: Receiver structure.

- 50A - where {d(n)} is the sequence of independent M-ary data symbols, T'is the signaling interval, and g(t) is the basic transmitter pulse usually bandlimited to 1/T. The signal from the transmitter is sent over A ^{' } diversity channels, which are assumed to be independently fading. The re¬ ceived signal in each of the channels is quadrature down- converted, lowpass filtered, and A/D converted. Prior to processing, signals from different channels are frame synchronized. This is accomplished using filters matched to the channel probe. The signaling format, containing the channel probe and the data block, is shown in Fig.l. After coarse alignment in time, the received signal in the i ^{th } diversity branch is represented as

Vi(t) = ∑ d{n)hi(t - nT, ήe^'W + »i(t) (2) n where & _{ι }(r, t) is the channel impulse response (including any transmit or receive filtering) as a function of delay r at time £, 0 _{» } (t) is the carrier phase, and Vi{t) is assumed to be white Gaussian noise.

The receiver structure is shown in Fig.2. The front section of the receiver consists of a bank of feedforward equalizers and a multichannel carrier synchronizer. Since the channel impulse responses /:, (£) are not known, there is no explicit matched filtering prior to equalization. The feedforward linear equalizers are fractionally spaced (FS), i.e. they operate on the sequence of input samples taken at time intervals less than T. An infinitely long feed¬ forward equalizer with optimal tap setting accomplishes both functions of matched filtering (adaptive, in case of time varying channels) , and optimal T-spaced linear equalization [5] . The most important feature of a FS feedforward section is that it is insensitive to the timing phase of the incomming signals, therefore eliminating the need for separate esimation of the symbol timing. Only if very long, or continuous messages are being transmitted, the need may arise for some sort of adaptive adjustment

- 50B - of the timing phase, in order to ensure the correct posi¬ tion of the center tap of the equalizer [6]. Without loss of generality, we use a fractional spacing of T/2, which is adequate for any signal bandwidth less than 1/T.

Although theoretically the optimally chosen complex tap weights of the linear equalizer correct for any phase offset in the received signal, this is not the case in prac¬ tice. The carrier phase in the i ^{th } channel, 0 _{X }(£), can be modeled as a sum of three terms: constant phase offset, Doppler frequency shift, and random phase jitter. While an adaptive equalizer is capable of correcting for the con¬ stant phase offset and possibly some slow variations of the carrier phase, the carrier frequency offset, as well as more rapid phase fluctuations, result in the equalizers tap rotation phenomenon [7]. This increases the misadjust- ment noise, and may eventually cause the equalizer taps to diverge. Typically, the tap gains should not change by more than few percent from one symbol interval to another [S]. Therefore, the addition of a carrier phase synchronization loop is necessary to ensure proper opera¬ tion of the equalizer, especially in the conditions of large phase fluctuations encountered in the UWA channels.

Due to the fact that the feedforward equalizer intro¬ duces a delay of a certain number N of symbol intervals, the current estimate of the carrier phase, #i(π), lags be¬ hind the true phase of the input signal, θi(nT + N _{\ }Tf2). It is for this reason that the carrier phase synchroniza¬ tion is performed after equalization, now termed pass¬ band equalization, thus eliminating the problem of delay in the phase estimate [7]. The feedforward equalizer out¬ put is produced once per symbol interval, and the car¬ rier phase update is performed accordingly. Depending on the particular channel characteristics, it may not be necessary to have a separate DPLL for each of the di¬ versity branches. In the application of interest, however, we found that due to the possibly large differences in time varying Doppler frequency offsets caused by unpre¬ dictable motion of the receiver array, it was necessary to have as many phase estimators as diversity channels.

- 51 -

This is also one of the reasons that preclude the use of a passband DFE structure [S] in the multichannel form. In this structure, the carrier phase correction is moved further into the decision feedback loop, resulting in some minor improvements.

After coherent combining, the signals from different channels are fed into the common decision feedback part of the equalizer. Such a structure resembles maximal ra¬ tio combining, in which each diversity signal is weighted proportionally to its strength, and coherently combined with the others prior to decision making [5]. Indeed, if there were no intersymbol interference (ISI), the two structures would be equivalent.

Since the channel is time varying, so are the optimal values of receiver parameters. An adaptive algorithm for joint estimation of equalizer coefficients and carrier phases is presented in the following section. The receiver initially operates in the training mode, using known data symbols, after which it is switched to a decision directed mode.

III. DERIVATION OF THE RECEIVER ALGORITHM

Having established the receiver structure, we can pro¬ ceed to determine the optimal values of its parameters. The optimization criterion we use is the minimum mean squared error (MSE) between the estimated data sym¬ bol d(n) and the transmitted symbol d(n). The receiver parameters are the tap weights of the multichannel feed¬ forward equalizer, feedback equalizer coefficients, and the carrier phase estimates. In general, there are two ways of computing the equalizer parameters. One is the direct adaptation of the equalizer coefficients driven by the out¬ put error, and the other is their computation from the estimated channel impulse response. Although the latter is potentially more robust to the time variations of the channel [9], we chose the usual, direct method, as com¬ putationally less involved.

- 51A -

Assuming the constant channel impulse response and carrier phase in some short interval of time, one arrives at the optimal values of equalization and synchronization parameters. Let the £* ^{h } channel feedforward equalizer tap weight vector be

J = [ _{iVl } - - α5 _{Va }r (3) where (•) denotes the conjugate transpose, and the tap weights are taken as conjugate for later convenience of notation. The input signal samples stored in the I ^{th } feed¬ forward equalizer at time nT are conveniently represented in a column vector

v,-(n) = [v(nT + NχT/2) • - - v(nT - N _{2 }T/2)] ^{T }. (4)

The output of the I ^{th } feedforward equalizer, after phase correction by the amount #,- , is given as

Pi(π) = a$vi (n)e-^' (5) and the coherent combination of all diversity channels is

K

The feedback filter coefficients are arranged as a vector

b ^{, } = [6i - - . ^{" }6A ]- (7) and the column vector of M previous decisions, currently stored in the feedback filter, is denoted as

d(n) = [d{n - 1) • • • d{n - M)] ^{τ } . (8)

This defines the output of the feedback filter as

q(n) = b'd(n). (9)

- 51B -

The estimate of the data symbol at time n is

d(n) = p(n) - q(n) (10)

from which the decision d(n) is obtained as the closest signal point. The estimation error is

e(n) = d(n) - d{n) (11) and the receiver parameters are optimized based on joint minimization of the MSE with respect to {a,}, b, and

In order to find the optimal values of the equalizer co¬ efficients, it is convenient to group all the coefficients into a composite vector c, and to express the estimate d(n) as

= c'u(π). ( 12)

The MSE can now be expressed as a function of the com¬ posite equalizer vector c,

E = £{|<i(n) - c'u(n)| ^{2 }} (13)

= R _{dd } - 2Re{c ^{, }H _{ud }] + c'R _{uu }C

where we have used the notation R _{ry } = E{x(n)y'(n)} for the crosscorrelations. The value of c which minimizes the MSE is the well known solution to the finite order Wiener filtering problem, and is given by

c = R _{u } - _{u }! H ^{• } _{ud } ( 14)

- 52 -

The optimal values of the estimates of the carrier phases, θι , are most easily found if the estimate <f(π) is represented as

d{n) = Pf(n) + _{Pi } (n) - ς(n) (15)

3≠i = a;v _{t }-(n)e-^' -+ Λ(π).

The second term in the last expression is independent of θ{ , which makes it possible to express the MSE as

= -2Λe{a'i£{v;(n) n) - fi(n)]' }e ^{' }^} 4- terms independent of θ{

The optimal values θ{ satisfy the gradient equations

• = -2/m{a5 {v,-(n)[d(n) - fi(n) )c ^{' }^ } = 0, (17) dOi i — 1, . . . , K. .

In order to be able to track the actually time varying optimal solution for the receiver parameters, the equa¬ tions (14), (17) should be solved recursively, using up¬ dated values of possibly time varying crosscorrelations. In the case of a rapidly changing channel, the adapta¬ tion has to be carried out continuously. An alternative method to continuous adaptation is the so called block adaptation [10], in which the receiver parameters are up¬ dated only during short training blocks interspersed in the data stream, and interpolated between such blocks. The adavantage of such an approach is the prevention of error propagation.

As it was pointed out earlier, the carrier recovery pro¬ cess can theoretically be absorbed in the proces of equal¬ ization. It can be verified that the optimal solution in such case would be the same as the one represented by equations (14), (17). The point of having separate expres-

- 52A -

sions for the equalizer coefficients and the carrier phases, is to be able to derive different tracking strategies for the two, which ultimately eliminates the problem of equalizer tap rotation.

The simplest form of an adaptive algorithm is the com¬ bination of a least mean squares (LMS) algorithm for the equalizer coefficients updata, and the first order DPLL [7]. Such an algorithm, however, failed on the UWA channel, primarily due to the poor phase tracking ca¬ pabilities. In order to obtain improved phase tracking capabilities, we introduced a second order DPLL into the process of joint synchronization and equalization. Using the analogy between the phase detector output of a clas¬ sical DPLL and the instantaneous estimate of the MSE gradient with respect to #,-, we define

_{£ }(n) = 7m{a;*£;{v _{l }-(n)[d(n)-/ _{l }(n)]-}e-^'} (IS) as the equivalent output of the i ^{th } phase detector. Using the fact that d(n) - fi(n) = _{Pi }(n) + e{n) (19) the expression (18) is rewritten as

Φi(n) + e(n)] ^{m }} _{% } i= l,...K. (20)

The second order phase update equations are given by

θi{n + 1) ____= §i(n) + K _{βl } i{n) + K _{β }_ ∑ Φ _{t }*( ), (21) msrO

*= 1..../C.

- 52B -

It is assumed here that the same proportional and integral tracking constants are used in all diversity channels. The update equation (21) corresponds to perfect loop integra¬ tion, while it is also possible to use imperfect integration as well as sliding window integration.

The equalizer coefficients are computed adaptively based on the RLS estimation principles. The RLS al¬ gorithms have become almost a standard in digital signal processing, due to their superior convergence properties over the LMS algorithm. The RLS algorithm solves for the equalizer tap weight vector as

c(n) = ^ (71)^(11) (22)

where the estimated crosscorrelation matrices are R _{y } = λ ^{n _m }x(n)y ^{, }(n), λ being the forgetting factor which accounts for the exponential windowing of the past data [11].

The long channel response (long equalizer) in conjunc¬ tion with diversity reception, results in the high compu¬ tational complexity of the standard RLS algorithm. A fast transversal filter (FTF) realization can be used in¬ stead for implementation. We have found a multichannel FTF algorithm presented in [12] readilly applicable for the problem at hand, with minor modifications concern¬ ing the incorporation of the carrier phases update equa¬ tions.

The exact performance analysis of the proposed re¬ ceiver configuration is hard to evaluate. The theoretical analysis of a similar receiver was carried out in [13] for the case of perfectly known channel responses. It is the subject of current study to evaluate the impact of estima¬ tion errors (possibly high for rapidly changing channels) on the overall receiver performance. Examining the op¬ timal values of the receiver parameters, shows that in each diversity branch, coherent combining of multipath components is performed, which results in implicit di-

- 53 -

versity improvement [13]. Further, signals from different (explicit) diversity channels are combined in a way anal¬ ogous to the maximal ratio combining. In other words, if one of the channels has high SNR relative to the others, it will be favored accordingly, while if there is a 'bad ^{* } chan¬ nel, with very low SNR, it will automatically be rejected in the process of adaptation.

IV. EXPERIMENTAL RESULTS

The proposed algorithm was tested and proved effi¬ cient on long range acoustic telemetry channels. The experiment was conducted by the WHOI, off the coast of California in January 1991. The data were transmit¬ ted through the deep water over several distances ranging from 40 to 140 nautical miles and corresponding to 1,2 and 3 convergence zones. The total transmitted power was lkW, and the data rate was varied from 3 to 333 symbols per second. The signals were received over a vertical array of 12 sensors spannning depths from 500m to 1500m.

The modulation format used in the analysis is QPSK and 8-QAM. The signal is shaped at the transmitter using a cosine roll-off filter with roll of factor 0.5, and truncation length of ±2 symbol intervals. The signals are formed using a sampling frequency of 4k z, and modulated onto a 1k z carrier. The transmission was organized in blocks (see Fig.l). The channel probe consisted of a 13 element Barker code with rectangular (unshaged) pulses, and the data block was generated using PN sequences.

The chioce of receiver parameters such as equalizer length, carrier phase tracking constants, and the forget¬ ting factor of the RLS algorithm, was based on a series of channel estimation experiments. Here we present several examples. Fig.3 presents results of single channel recep¬ tion for purposes of later comparison. It refers to QPSK transmission at 333 symbols per second over 110 nautical miles, channel 8. The channels (hydrophones of the ar¬ ray) are numbered O ÷ 11, channel 0 being the one closest

- 53A -

to the surface. Shown in the figure are the input scat¬ ter plot, the mean squared error, the phase estimate and the output scatter plot. The input SNR, measured from the Barker probe, was on the order of !4.dB. The scatter plot of the input signal is completely smeared due to the ISI, phase fluctuations and noise. The ISI at 110 nautical miles was measured to span about 60ms, or 20 symbol intervals at the rate 333 symbols per second. The MSE indicates convergence of the algorithm in about 100 sym¬ bol intervals. The estimated phase is shown as a function of time measured in symbol intervals, after the constant Doppler shift has been removed. The output SNR, mea¬ sured from the scatter plot of the estimated data symbols, was 12dB, and the block error probability is estimated to be on the order of 2 • 10~ ^{4 }. The used receiver parameters are indicated in the figure. The length of a feedforward equalizer is denoted by N, and the center tap was posi¬ tioned in the middle.

The signal from channel 8 and the signals from chan¬ nels 6 and 10 of similar characteristics and single chan¬ nel performance, were processed by a multichannel algo¬ rithm, and the result is shown in Fig.4. The expected convergence period can be estimated as twice the total number of taps which is about 250 symbol intervals. The estimated phases are shown after the individual Doppler shifts of -0.18Hz, -0.21Hz, and -0.22Hz were removed. The output scatter plot shows noticeable improvement in

- 53B -

Figure 3: Results for QPSK, 333 symbols per second, 110 nautical miles, channel 8. Receiver parameters: N = 40, M = 10, λ = 0.99, A'* _{t } = 0.001 , K _{θ }_ = 0.0001.

performance of about 5dB, which is to be expected for the third order diversity. There were no decision errors in this case.

Finally, Fig.5 shows multichannel results obtained with an 8-QAM signal constellation at the same rate and range. In this case, the SNR per single channel was in¬ sufficient, and multichannel processing was necessary to ensure proper operation. The output scatter plot shows successfull operation of the algorithm, with output SNR of 13.5< S, and the probability of error on the order of 10- ^{3 }.

Satisfactory results were also obtained at lower rates and ranges. An attempt was made to demodulate data transmitted at 1000 symbols per second. However, the performance was severely limited by very poor SNR.

- 54 -

V. SUMMARY AND CONCLUSIONS

In the attempt to achieve reliable digital communi¬ cations over long range UWA channel, we have pro¬ posed a receiver algorithm for joint, multichannel carrier phase synchronization and decision feedback equalization, based on multiparameter estimation techniques. The re¬ ceiver features a second order multichannel DPLL, and an RLS adaptation of the equalizer coefficient suitable for implementation in FTF version.

The algorithm was successfully applied to the experi¬ mental long range telemetry data transmitted at rates up to 333 symbols per second, over distances covering 1, 2 and 3 convergence zones. The experimental results assert the fesibility of simultaneously combatting the extended ISI, and removing the phase fluctuations, thus coherently combining the multiple arrivals in each of diversity chan¬ nels. Additional improvement with respect to fading and

Figure 4: Results for QPSK, 333 symbols per second, 110 nautical miles, channels 6,8 and 10. Receiver parameters: N = 40, M = 10, A = 0.99, K _{θ χ } = 0.001, K _{β }_ - 0.0001.

- 54A -

Figure 5: Results for 8-QAM, 333 symbols per second, 110 nautical miles, channels 8 and 10. Receiver param¬ eters : N = 40, = 10, λ = 0.99, K _{β l } = 0.001, K _{β }, = 0.0001.

noise, which are the major limiting factors for the UWA telemetry, is achieved through the use of spatial diversity.

- 54B -

References

[l] J. Catipovic, "Performance limitations in underwater acoustic telemetry," IEEE J. Oceanic Eng. vol. OE- 15, pp. 205-216, July 1990.

[2] H.Kobayashi, "Simultaneous adaptive estimation and decision algorithms for carrier modulated data trans¬ mission systems," IEEE Trans. Comm. vol. COM-19, pp. 268-280, June 1971.

[3] G.Ungerboeck, "Adaptive maximum likelihood re¬ ceiver for carrier modulated data-transmission sys¬ tems," IEEE Trans. Comm. vol. COM-22, pp. 624- 636, May 1974.

[4] M.Stojanovic, J. Catipovic and J. Proakis, "Coherent communications over long range acoustic telemetry channels," in NATO AS I Series on Acoustic Sig¬ nal Processing for Ocean Exploration, J.Moura and I.Lourtie Eds., in press.

[5] J. Proakis, Digital Communications, McGraw-Hill 1989.

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