BACKGROUND

[0001] Hydrocarbon fluids such as oil and natural gas are obtained from a subterranean geologic formation, referred to as a reservoir, by drilling a well that penetrates the hydrocarbon-bearing formation. Once a wellbore is drilled, various forms of well completion components may be installed to control and enhance the efficiency of producing the various fluids from the reservoir. Data representative of various downhole parameters, such as downhole pressure and temperature, are often monitored and communicated to the surface during operations before, during and after completion of the well, such as during drilling, perforating, fracturing, and well testing operations. In addition, control information often is communicated from the surface to various downhole components to enable, control, or modify the downhole operations.

[0002] Accurate and reliable communications between the surface and downhole components during operations can be difficult. Wireline communication systems can be used in which electrical or optical signals are transmitted via a cable. However, the cable used to transmit the communications generally requires complex connections at pipe joints and to traverse certain downhole components, such as packers. In addition, the use of a wireline tool is an invasive technique which can interrupt productions or affect other operations being performed in the wellbore. Thus, wireless communication systems can be used to overcome these issues.

[0003] An example of a wireless system is an acoustic communication system. In acoustic systems, information or messages are exchanged between downhole components and surface systems using acoustic transmission mediums. As an example, a network of acoustic devices can be deployed downhole that uses tubing in the wellbore as the medium for transmitting information acoustically.

SUMMARY

[0004] Certain embodiments of the present disclosure are directed to a method of communicating in a multicarrier wireless communication system that includes a plurality of wireless modems that exchange messages on a wireless communications medium deployed in a borehole. In accordance with the method, a first wireless modem generates a wideband wireless signal to transmit a message on the wireless communication medium deployed in the borehole. The wideband wireless signal carries information associated with the message in data frames. Each data frame includes a payload portion containing message data corresponding to at least a portion of the message and a preamble portion that is based on a Zadoff-Chu sequence. The first wireless modem transmits the wideband wireless signal on the wireless communications medium for receipt by a second wireless modem. The second modem detects the data frames based on the preamble portion.

[0005] Further embodiments of the present disclosure are directed to a system for performing a downhole operation in a wellbore. The system includes a control and telemetry system to control and monitor a downhole operation, downhole equipment located in the wellbore to observe a parameter of interest associated with the downhole operation, and first and second acoustic modems coupled to an acoustic transmission medium at respective locations extending between the control and telemetry system and the downhole equipment. In response to receipt of a message directed to the downhole equipment, the first acoustic modem generates information representing the message and distributes the information in data frames across a wideband acoustic signal. Each data frame includes a payload portion containing message data and a preamble that is based on a Zadoff-Chu sequence.

[0006] Yet further embodiments of the present disclosure are directed to a method of communicating in a multicarrier acoustic communication system that includes a plurality of acoustic modems that exchange messages on an acoustic communications medium deployed in a borehole. The method includes generating, by a first acoustic modem, a wideband acoustic signal to transmit a message on the wireless communication medium. The wideband acoustic signal carries information associated with the message in data frames. Each data frame includes a payload portion and a preamble that includes a first preamble signal, a second preamble signal and a third preamble signal. Each of the first, second and third preamble signals are repetitions of a Zadoff-Chu sequence. The first modem transmits the wideband acoustic signal and a second modem receives the wideband acoustic signal. The second acoustic modem estimates a clock frequency offset between the first and the second acoustic modems based on the first, second and third preamble signals.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Certain embodiments of the invention are described with reference to the accompanying drawings, wherein like reference numerals denote like elements. It should be understood, however, that the accompanying drawings illustrate the various implementations described herein and are not meant to limit the scope of various technologies described herein. The drawings show and describe various embodiments of the current invention.

[0008] Fig. 1 is a schematic illustration of a downhole wireless communications system, in accordance with an embodiment.

[0009] Fig. 2 is a schematic illustration of an acoustic modem that can be deployed in a downhole wireless communications system, in accordance with an embodiment.

[0010] Fig. 3 is a block diagram illustrating a multi-carrier communication technique, in accordance with an embodiment.

[0011] Fig. 4 is a block diagram illustrating further details of a multi-carrier modulation procedure of Fig. 3, in accordance with an embodiment.

[0012] Fig. 5 is a block diagram illustrating further details of a multi-carrier demodulation procedure of Fig. 3, in accordance with an embodiment.

[0013] Fig. 6 illustrates a structure of a frame that can be used to communicate information in the wireless communications network of Fig. 1 when a multi-carrier communication procedure is implemented, according to an embodiment.

[0014] Fig. 7 depicts a process flow for extending the range of a clock frequency offset estimation implemented by a receiving acoustic modem, according to an embodiment. DETAILED DESCRIPTION

[0015] In the following description, numerous details are set forth to provide an understanding of the present invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these details and that numerous variations or modifications from the described embodiments may be possible.

[0016] In the specification and appended claims: the terms“connect”,“connection”, “connected”,“in connection with”, and“connecting” are used to mean“in direct connection with” or“in connection with via one or more elements”; and the term“set” is used to mean “one element” or “more than one element”. Further, the terms “couple”, “coupling”, “coupled”, “coupled together”, and“coupled with” are used to mean“directly coupled together” or“coupled together via one or more elements”. As used herein, the terms“up” and “down”, “upper” and “lower”, “upwardly” and downwardly”, “upstream” and “downstream”; “above” and“below”; and other like terms indicating relative positions above or below a given point or element are used in this description to more clearly describe some embodiments of the invention.

[0017] Wireless communication networks can be used to transmit information or messages between, for instance, a control and telemetry system and various tools or other devices. When a wireless communication network is used in a hydrocarbon exploration, testing or production environment, the control and telemetry system typically is located at the surface and the tools or other devices are located downhole in a wellbore. The tools and devices are referred to as downhole equipment and can include, for example, packers, valves, chokes, firing heads, perforators, samplers, pressure gauges, temperature sensors, flow meters, and fluid analyzers. Messages exchanged between the surface system and the downhole equipment can be used to operate the equipment (e.g., a valve or a firing head), to control the performance of a downhole operation, or to monitor various downhole conditions before, during or after an operation, such as fluid flow, tool status, temperature, pressure, and fluid composition.

[0018] One type of wireless communications network that can be used to exchange messages between the surface and downhole equipment is an acoustic communication network. Fig. 1 shows a schematic view of an acoustic communication network that is deployed in a hydrocarbon well. It should be understood that the systems and techniques described herein are applicable throughout the life of the well, including during drilling, logging, drill stem testing, fracturing, stimulation, completion, cementing and production.

[0019] Referring to Fig. 1 , a network of modems 102a-f is deployed in a wellbore 104 so that information can be exchanged between a surface control and telemetry system 106 and downhole equipment along both a downlink (from the surface to the downhole equipment) and an uplink (from the downhole equipment to the surface). The surface control and telemetry system 104 can include processing electronics, a memory or storage device and transceiver electronics to transmit and receive messages to and from the network of modems 102a-f via a wired connection 108. In various embodiments, the processing electronics can include a signal conditioner, filter, analog-to-digital converter, microcontroller, programmable gate array, etc. The memory or storage device can store telemetry data received from the downhole equipment so that it can be processed and analyzed later. Yet further, the memory or storage device can store instructions of software for execution by the processing electronics to generate messages to control and monitor performance of a downhole operation.

[0020] The modems 102a-f are acoustically coupled to an elastic medium, such as tubing 1 10, which can be a jointed pipe string, production tubing, or a drill string, that provides the acoustic communications path. It should be understood, however, that the elastic medium may be provided by other structures, such as a tubular casing 1 12 that is present in the wellbore 104, or by platform risers for subsea hydrocarbon well applications.

[0021] Because of the acoustic loss inherent to the elastic medium, communications in one hop from surface to downhole and vice versa generally are not feasible. Thus, a network of modems 102a-f is deployed to effectuate the downlink and uplink communications, where the modems 102a-f relay the messages that propagate along the transmission path or tubing 1 10.

[0022] In addition to the modems 102a-f, the installation shown in Fig. 1 includes a packer 1 14 positioned on the tubing 1 10 at a region of interest 1 16. Various pieces of downhole equipment for testing and the like are connected to the tubing 1 10, either above or below the packer 1 14, such as a test valve 1 18 above the packer 1 14 and a sensor 120 below the packer 1 14.

[0023] The modems 102a-f, which are part of the acoustic communications network, are made of electrical and mechanical components that provide the ability to transmit and receive acoustic signals that are exchanged between the surface and the downhole equipment. A schematic illustration of a modem 102 is illustrated in Fig. 2. Modem 102 includes a housing 122 that supports an acoustic transceiver assembly 124 that includes electronics and a transducer 126 which can be driven to create an acoustic signal in the tubing 1 10 and/or excited by an acoustic signal received from the tubing 1 10 to generate an electrical signal. The transducer 126 can include, for example, a piezoelectric stack, a magneto restrictive element, and/or an accelerometer or any other element or combination of elements that are suitable for converting an acoustic signal to an electrical signal and/or converting an electrical signal to an acoustic signal. The modem 102 also includes transceiver electronics 128 for transmitting and receiving electrical signals. Power can be provided by a power supply 130, such as a lithium battery, although other types of power supplies are possible, including supply of power from a source external to the modem 102.

[0024] The transceiver electronics 128 are arranged to receive an electrical signal from and transmit an electrical signal to the downhole equipment, such as the sensor 120 and the valve 1 18. The electrical signal can be in the form of a digital signal that is provided to a processing system 132, which can encode and modulate the signal as will be described herein, amplify the signal as needed, and transmit the encoded, modulated, and amplified signal to the transceiver assembly 124. The transceiver assembly 124 generates a corresponding acoustic signal for transmission via the tubing 1 10.

[0025] The transceiver assembly 124 of the modem 102 also is configured to receive an acoustic signal transmitted along the tubing 1 10, such as by another modem 102. The transceiver assembly 124 converts the acoustic signal into an electric signal. The electric signal then can be passed on to processing system 132, which processes it for transmission as a digital signal to the downhole equipment. In various embodiments, the processing system 132 can include a signal conditioner, filter, analog-to-digital converter, demodulator, modulator, amplifier, encoder, decoder, microcontroller, programmable gate array, etc. The modem 102 also can include a memory or storage device 134 to store data received from the downhole equipment so that it can be transmitted or retrieved from the modem 102 later. Yet further, the memory or storage device 134 can store instructions of software for execution by the processing system 132 to perform the various modulation, demodulation, encoding, and decoding, techniques described herein.

[0026] Returning to Fig. 1 , the acoustic channel provided between each pair of modems, such as modem 102a and modem 102b, has a characteristic transfer function that is composed of passbands (a frequency band in which signals are reliably transmitted along the channel) and stopbands (a frequency band in which signals are not reliably transmitted along the channel). For example, a transfer function that is typical of a pipe string deployed in a hydrocarbon well has bands having widths in the range of 50 Flz to 150 Hz. Generally, the pipe lengths and pipe joint dimensions of the pipe string are the main characteristics that drive the location of the center frequencies of the passbands and stopbands, which can be, as examples, anywhere in the range where acoustic communications are possible.

[0027] In the illustrative embodiments described herein, the messages exchanged between the surface and the downhole equipment can encompass control signals, polls for data, tool status information, and measurements provided by sensors. In general, the messages that are communicated are made up of a sequence of digital bits. To transmit the bits between components, the bits are transformed into a form suitable for acoustic transmission. That is the bits are transformed so that the information can be carried on an acoustic wave that propagates along the elastic structure that serves as the acoustic transmission medium. The technique for performing the transformation is generally referred to as modulation.

[0028] In many instances, it is difficult to predict the transfer function of the acoustic transmission path before the network is actually installed, which makes it difficult to select an optimal carrier frequency on which to modulate information. A further complicating factor is that the optimal carrier frequency may not be the same for all portions of the acoustic transmission path. For instance, in a wellbore, the characteristics of the tubular string that is used for the transmission path vary along its length as different sections of the string often have structural characteristics (e.g., different pipe lengths) that are different than other sections.

[0029] To address this issue, frequency diversity techniques can be used to effect communications on the acoustic transmission medium. In general, frequency diversity refers to a wideband signal carried on a communications channel that spans a range of frequencies. The bandwidth of the wideband signal can span at least one passband, or both one or more passbands and one or more stopbands. Different modulation techniques can be used to spread or distribute the information across the bandwidth and, thus, to achieve the wideband communication channel. Such techniques include, for example, spread spectrum techniques (e.g., frequency hopping) and orthogonal frequency division multiplexing (OFDM), where multiple, closely spaced orthogonal subcarrier signals are used to carry the bits of information in parallel channels or streams.

[0030] When frequency diversity is used, the information that makes up the message can be spread over a wide bandwidth in a manner that ensures that the original message can be recovered even though some of the information may be transmitted in regions of the acoustic channel that are subject to frequency-selective fading (i.e. , the stopbands). The central frequency of the wideband signal can be chosen independently of the acoustic characteristics and configuration of the transmission medium and environment in which the acoustic network is deployed. Thus, the central frequency of the wideband signal can be chosen at the system design level based on parameters, such as average energy in the acoustic channels, expected power spectral density of acoustic noise that may be present in the environment, and design of the piezoelectric sensor. The central frequency can also be optimized based on the operation that will be performed. For example, if a drilling operation is to be performed, the drill pipes will have significantly different acoustic transfer functions than production tubing so that the central frequency for communications during a drilling operation may be different than the central frequency used for communications during production or testing. [0031] In embodiments in which the acoustic network is implemented in a hydrocarbon well, the width of one passband typically is in the range of 50-150 Hz and the combined width of one passband and one stopband typically may span a region of 100 - 300 Hz. Thus, in embodiments in which the acoustic communications channel is configured to have a bandwidth that encompasses at least one passband and at least one stopband, the bandwidth of the wideband acoustic signal is at least 300 Hz. However, other bandwidths of the wideband acoustic signal are contemplated and can, for instance, have a span that is an order of magnitude larger, such as 1000 Hz to 2000 Hz. The components (e.g., symbols) of the wideband signal representing the information to be exchanged between the surface and the downhole equipment are spread across that bandwidth.

[0032] As mentioned, any one of a variety of available modulation techniques, including spread spectrum techniques and OFDM, can be used to distribute the symbols across the bandwidth of the acoustic signal. When using OFDM, a sequence of bits representing the original message is encoded and mapped to symbols that are distributed over multiple orthogonal subcarriers. A variety of constellation mapping techniques are available for mapping bits to symbols based, for instance, on amplitude and phase information. These techniques include phase shift keying, amplitude shift keying, a combination of phase shift and amplitude shift keying, or other mapping techniques. In general, a fixed number of bits can be mapped to one symbol, where the number of bits depends on the type of mapping scheme used. For example, when a Quadrature Phase Shift Keying (QPSK) mapping scheme is used, two bits can be mapped into one symbol. When 16QAM is used, four bits are mapped into a symbol, increasing the bit rate by a factor of two when compared to QPSK.

[0033] In embodiments described herein, various error correction coding and processing techniques can be used with frequency diversity to code the sequence of bits of the original signal into encoded bits that are then mapped to the symbols. Error correction coding increases the likelihood that the original message can be recovered at the receiver. As examples, the error correction coding and processing can include Forward Error Correction (FEC) coding, maximal combining ratio coding, and other suitable coding techniques or combinations of techniques known or that may become available.

[0034] FEC encodes or transforms a sequence of bits into a longer sequence of different bits. The encoding process results in each of the original message bits being reflected in each of the encoded bits, thus intrinsically providing for redundancy in the transmitted information. As a result, if some of the encoded bits are lost or corrupted during transmission due to noise or frequency fading, the original message bits may still be recovered from the remaining bits in the decoding process. FEC coding includes block coding, and convolutional coding, and can be systematic, or not systematic. When FEC is used with frequency diversity, the original sequence of bits is encoded and then distributed across the bandwidth of the acoustic signal. For example, when OFDM is used, the information representing the original message can be distributed over different time slots and different subcarrier frequencies in the frequency band of the wideband channel.

[0035] Maximal combining ratio coding techniques, on the other hand, rely on actual redundancy to increase the likelihood that information can be recovered. For example, the complete information representing the original message is transmitted multiple times, thus increasing the probability that the original message can be recovered. When used with frequency diversity, the same symbols representing the original information can be transmitted on multiple subcarrier frequencies. In other words, the message is transmitted multiple times. Upon receipt by the decoder, soft information regarding the received symbols can be determined (e.g., frequency, phase, and norm) and then used to weight the received symbols. The weighting provides an indication of reliability or confidence that the symbol has been properly received. The weighted symbols on each of the subcarriers can then be mathematically combined to recover the original message.

[0036] When an encoding scheme, such as FEC, is used with the modulation techniques, such as OFDM, the original bits of the signal are encoded, mapped to symbols, and then multiplexed in time and frequency to spread the information across the bandwidth in a manner that provides for efficient and reliable recovery of the original information. The code rate of the encoding scheme (i.e. , the ratio of original message bits to encoded bits) is selected based on the bandwidth of the channel. That is, the code rate is selected so that it is enough to provide for reliable recovery of the original message even though a portion of the coded information is located in one or more stopbands.

[0037] Embodiments described herein can also employ an interleaver to randomize the location of the encoded information across the bandwidth, and, thus, to increase the time and frequency diversity of the communication scheme. Different types of interleavers can be used, including pseudo random interleaving, periodic interleaving and convolutional interleaving.

[0038] Fig. 3 is a block diagram of illustrative transmission and reception techniques that are implemented by and between modems 102 in the network in order to transmit a wideband signal representing a message. In block 200, the transmitting modem (e.g., modem 102a) applies an error coding scheme (e.g., FEC) to encode the sequence of“k” bits representing the original message into a sequence of“n” bits, where (n>k). In block 202, the“n” bits are then processed and modulated (e.g., mapped to symbols, multiplexed in time and frequency) for multi-frequency transmission as an acoustic message on the acoustic network.

[0039] During transmission on the medium (block 204), the wideband acoustic signal is affected by the transfer function of the acoustic transmission medium and by noise that is present in the environment. At block 206, upon receipt of the wideband signal by the receiving modem (e.g., modem 102b), the receiver demodulates the symbols and calculates soft information characterizing the received symbols, such as frequency, phase, amplitude, and norm. The soft information is indicative of whether the received symbol has been properly received. For instance, if the received symbol is transmitted on a subcarrier that is in a passband, then the amplitude of the symbol should be relatively high. Thus, a high amplitude is indicative a high degree of confidence that the symbol is reliable.

[0040] The soft information is then provided to a decoder (block 208) to derive the original sequence of “k” bits that represents the message. If a convolutional coder was employed to code the original“k” bits at block 200, then the decoding in block 208 is performed by a convolutional decoder.

[0041] In some embodiments, the decoding in block 208 can be performed in two phases, where a convolutional decoder is employed in one of the phases and maximal combining ratio is employed in another of the phases. The soft information provides an indication of the reliability and, thus, can be used to weight the received symbols. The maximal combining ratio technique can then combine the weighted information received on the various subcarriers in order to increase the likelihood that the“k” original bits representing the message can be recovered. When convolutional decoding is used with a maximal combining ratio technique, the amount of redundant information that is included in the acoustic message can be reduced. Consequently, embodiments which employ both techniques in the decoding process can achieve higher data transmission rates.

[0042] Fig. 4 is a block diagram providing additional detail regarding the processing performed in the multi-frequency modulation block 202 of Fig. 3. In block 210, the coded sequence of “n” bits is mapped to symbols using a constellation mapping scheme. In block 210, the mapping assumes that“M” bits are mapped to each symbol, so that a sequence of Ns = n/M symbols is generated. The sequence of Ns symbols is then time and frequency multiplexed with Nf frequencies (block 212), so that the wideband signal is represented by parallel Nf streams of Np = Ns/Nf symbols, where each Nf stream is to be transmitted on one of the subcarrier frequencies Fi ... FNf. At block 214, the Np sets are processed for multi-carrier transmission on each of the acoustic subcarrier frequencies.

[0043] Fig. 5 is a block diagram providing additional detail regarding the processing performed in the multi-frequency demodulation block 206 in the receiving modem of Fig. 3. The multi-carrier acoustic signal is received at block 216 and processed (e.g., to convert the received acoustic information into electrical information, synchronize the information between subcarriers, etc.) to derive parallel Nf streams of Np = Ns/Nf symbols. At block 218, the Nf streams are de-multiplexed in time and frequency to generate Ns sets of soft information representing the Ns symbols from which the original “k” bits of the message can be derived. [0044] The procedure for deriving the soft information assumes that the modems 102a, 102b synchronize in time and frequency, which can be accomplished using known telecommunications techniques. The synchronization information can be carried in the preambles of the information conveyed on various of the subcarrier frequencies. Amplitude and phase references also can be calculated for all subcarriers of the multi carrier signal in a“channel estimation” process. This information also can be carried in the preambles.

[0045] The synchronization and channel estimation information can then be used to derive the soft information for the received symbols. On each subcarrier frequency, each symbol is characterized by amplitude and phase. This amplitude and phase can be normalized by the reference phase and amplitude that has been estimated for that same subcarrier. The absolute and normalized values regarding amplitude and phase provide the soft information regarding the received symbol. The soft information also can be defined by other indicators, such as the position of the symbol on the constellation map, or others.

[0046] The soft information can then be used to determine which symbols were received on a subcarrier in a passband, and which symbols were received on a subcarrier in a stopband. The norm of the received symbol relative to the other symbols on a different subcarrier provides an indication of the location of the subcarrier in either a stopband or a passband. That is, a high norm relative to other subcarriers indicates that the subcarrier is located in a passband, and a relatively low norm indicates that the subcarrier is located in a stopband. The likelihood of the received bits of a given symbol can be weighted by the norm of the symbol so that symbols received on passband subcarriers are given more consideration than symbols that are received on stopband subcarriers.

[0047] Using the previous techniques, communication from one modem 102 to the next modem 102 can be achieved without knowledge of the characteristics of the transmission medium. The bandwidth of the wideband multi-carrier signal is chosen independently of the environment in which the acoustic network is deployed and can be fixed and chosen at the system design level based on estimated parameters, such as average energy in the acoustic channels, power spectral density of acoustic noise in the environment, design of the characteristics of the piezoelectric sensor, etc. The selected bandwidth can be a universal bandwidth, meaning that it is employed for communication on all segment or portions of the acoustic network.

[0048] However, even with the frequency diversity techniques set out above, fast and reliable communications in the passband/stopband acoustic channels can be challenging. For example, as mentioned previously, derivation of the soft information that is used by the decoder to derive the original message is based on an assumption that the modems are synchronized in time and frequency. However, in practice, there may be clock frequency offsets (CFOs) between modems which can then affect the reliability of frame detection and derivation of the soft information. For example, large CFOs can arise due to manufacturing-time tolerance, aging, or hardware damage during a job. In addition, temperature can also affect clock frequency, such that there can be large CFOs between modems in the network that are operating at different temperatures. Further, the presence of noise in the communication network can affect the reliability of frame detection . Accordingly, techniques and systems described herein are directed to enhancing the reliability of communications in passband/stopband acoustic channels. While these techniques and systems will be described below in the context of communication systems implemented in hydrocarbon well applications, the techniques and systems can be employed in any application in which wideband multicarrier communications are used.

[0049] Messages in the multicarrier communication systems described herein are transmitted using frames, where a message’s payload is transmitted in one or more message blocks, each message block formed by a cyclic prefix and a data symbol. An example structure of a frame 300 is depicted in Fig. 6. In this example, frame 300 includes preamble portions 302, 304, 306; a header 308; a cyclic prefix 312; and a message block 310 formed of a data symbol portion 31 1 and a cyclic prefix 314. In the example of Fig. 6, the header 308 is encoded using QPSK modulation and contains bits to indicate the length and modulation type of the data symbol(s) carried in the message block(s) 310. In embodiments, 16QAM or other modulation types can be used to modulate the data symbols in message block 310. [0050] The preambles 302, 304, 306 of frame 300 are signals used by a receiving modem to detect the frame and to perform fine synchronization, channel estimation and CFO estimation. In this embodiment, preambles 302, 304, 306 are repetitions of identical signals. As will be further described below, the signals in preambles 302, 304, 306 are based on Zadoff-Chu sequences. Due to the use of Zadoff-Chu sequences, the effects of both CFO and signal distortion can be mitigated.

[0051] Zadoff-Chu sequences belong to the class of constant amplitude zero autocorrelation (CAZAC) sequences. Zadoff-Chu sequences are complex-valued chirp signals which provide very low peak-to-average power ratio (PAPR) during the transmission of the frame detection preambles 302, 304, 306. Although Zadoff-Chu sequences are used in the description of the techniques and systems described below, other sequences that are currently known or that may be later developed having the same types of properties as Zadoff-Chu sequences also can be used.

[0052] The general expression of Zadoff-Chu sequences is as follows: for N even

for N odd

where n = [0..N-1], the constant r is coprime to N, and q is any integer.

[0053] Zadoff-Chu sequences have the following properties:

• Their cyclic autocorrelation equals zero for lags different from zero.

• The discrete Fourier transform (DFT) of a Zadoff-Chu sequence is also a Zadoff-Chu sequence.

• When r=N-1 , a cyclic time shift is equivalent to a modulation of the sequence.

This property makes this specific Zadoff-Chu sequence insensitive to frequency offsets. The effect of CFO is translated into a time shift, which is absorbed into the cyclic prefix of the OFDM symbol.

[0054] The use of Zadoff-Chu sequences in the preambles 302, 304, 306 for frame detection itself supports a large CFO offset by permitting frame detection under large CFO conditions. In addition, the Zadoff-Chu sequences also facilitate widening the range of the CFO estimation that is performed over the two final repetitions of the preamble (i.e., preamble blocks 304, 306 with sequences d [n] and c2[n]).

[0055] Fig. 7 is a block diagram of a technique 320 for extending the range of the CFO estimation. To estimate the CFO, the fast Fourier transform (FFT) of d [n] and c2[n] is determined, resulting in C1 and C2, respectively. At block 322, an initial angle estimate Fo is determined based on the average angle of C2 and CT. Flowever, this initial estimate cannot identify phase wraps, because it uses the average angle of the subcarriers. In embodiments, the true sign of phases beyond ±p can be determined by implementing a an algorithm that permits estimation of a linear phase function in the presence of noise, because this information is contained in the frequency-domain slope of the phases, which has the same sign as the true CFO.

[0056] Thus, after the initial CFO estimate, three hypotheses can be tested: a first hypothesis can use the initial phase estimate Fo (block 324); the second hypothesis uses the initial estimate Fo“+2tt” (block 326); and the third hypothesis uses the initial estimate Fo“-2tt” (block 328). Fitting errors are then calculated for each hypothesis (blocks 330, 332, 334). The result that provides the minimum squared error is used as the final CFO estimate (block 336).

[0057] This technique can double the range of the CFO estimation. In embodiments, the technique shown in Fig. 7 can be extended to allow the estimation of very large CFOs by adding further hypothesis tests over consecutive multiples of “2TT”.

[0058] It should be understood that the process represented in the flow diagram of Fig. 7 is an example and that variations of the depicted process can be implemented to extend the range of the CFO estimate. The blocks shown in Fig. 7 also can include more or fewer steps. Some blocks can be processed in parallel. Further, in the foregoing description, data and instructions for performing the various processes are stored in respective storage devices (such as, but not limited to, the storage device 134 associated with the modem 102 in Fig. 2) which are implemented as one or more non-transitory computer-readable or machine-readable storage media. The storage devices can include different forms of memory including semiconductor memory devices; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); ROM, RAM, or other types of internal storage devices or external storage devices. The stored instructions can correspond to the CFO estimation schemes described herein and can be executed by a suitable processing device, such as, but not limited to, the processing system 132 in Fig. 2. The processing device can be implemented as a general purpose processor, a special purpose processor, a microprocessor, a microcontroller, and so forth, and can be one processor or multiple processors that execute instructions simultaneously, serially, or otherwise.

[0059] It should further be understood that the techniques described herein can be implemented in a variety of wireless communications systems, and that the physical layer of the communication is not limited to the acoustic telemetry system that has been described above. Further, single or multi-carrier modulation systems can be used in any wireless communication system. As an example, orthogonal frequency division multiplexing (OFDM) is a modulation technique that is suitable for frequency selective channels. Flowever, embodiments disclosed herein are not limited to the use of any particular type of modulation system.

[0060] Although the preceding description has been described herein with reference to a limited number of embodiments, it is not intended to be limited to the particulars disclosed herein; rather those skilled in the art, having the benefit of this disclosure, will appreciate numerous modifications and variations therefrom. It is intended that the appended claims cover such modifications and variations as fall within the true spirit and scope of the invention.