HIGH SPEED OPTICAL MODEM.

BACKGROUND OF THE INVENTION.

1 . Field of the invention.

The present invention relates to the field of high-speed optical modem stable and robust systems capable of being retro-fitted, offering increased capacity and ensuring input/output reconfigurability.

2. Description of the related art.

It is known to use optical orthogonal frequency division multiplexing (OFDM) modulation technique in order to reduce optical modal dispersion in multimode fibre (MMF) transmission links, as disclosed for example in Jolley et al. (N.E. Jolley, H. Kee, R. Richard, J. Tang, K. Cordina, presented at the National Fibre Optical Fibre Engineers Conf., Annaheim, CA, March 1 1 , 2005, Paper OFP3). It offers the advantages of great resistance to dispersion impairments, efficient use of channel spectral characteristics, cost-effectiveness due to full use of mature digital signal processing (DSP), dynamic provision of hybrid bandwidth allocation in both the frequency and time domains, and significant reduction in optical network complexity.

It can also be used advantageously for dispersion compensation and spectral efficiency in single mode fibre (SMF)-based long distance transmission systems such as described for example by Lowery et al. (A.J. Lowery, L. Du, J. Armstrong, presented at the National Fibre Optical Fibre Engineers Conf., Annaheim, CA, March 5, 2006, paper PDP39) or by Djordjevic and Vasic (I.B. Djordjevic and B. Vasic, in Opt. express, 14, n ^Q 9, 37673775, 2006).

The transmission performances of OOFDM have been studied and reported for all the optical network scenarios including long-haul systems such as described for example in Masuda et al.( H. Masuda, E. Yamazaki, A. Sano, T. Yoshimatsu, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, Y. Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, T. Yamada, and S. Kamei, "1 3.5-Tb/s (1 35x 1 1 1 -Gb/s/ch) no-guard-interval coherent OFDM transmission over 6248km using SNR maximized second-order DRA in the extended L- band," Optical Fibre Communication/National Fibre Optic Engineers Conference (OFC/NFOEC), (OSA, 2009), Paper PDPB5) or in Schmidt et al. (B.J.C. Schmidt, Z. Zan, L.B. Du, and A.J. Lowery, "100 Gbit/s transmission using single-band direct-detection optical OFDM," Optical Fibre Communication/National Fibre Optic Engineers Conference (OFC/NFOEC), (OSA, 2009), Paper PDPC3) or metropolitan area networks such as described for example in Duong et al. (T. Duong, N. Genay, P. Chanclou, B. Charbonnier, A. Pizzinat, and R. Brenot, "Experimental demonstration of 10 Gbit/s for upstream transmission by remote modulation of 1 GHz RSOA using Adaptively Modulated Optical OFDM for WDM-PON single fiber architecture," European Conference on Optical Communication (ECOC), (Brussels, Belgium, 2008), PD paper Th.3.F.1 ) or in Chow et al. (C.-W. Chow, C.-H. Yeh, C.-H. Wang, F.-Y. Shih, C.-L. Pan and S. Chi, "WDM extended reach passive optical networks using OFDM-QAM," Optics Express, 16, 12096-12101 , July 2008) , or local area networks such as described for example in Qian et al. (D. Qian, N. Cvijetic, J. Hu, and T. Wang, "108 Gb/s OFDMA-PON with polarization multiplexing and direct-detection," Optical Fibre Communication/National Fibre Optic Engineers Conference (OFC/NFOEC), (OSA, 2009), Paper PDPD5) or in Yang et al. (H. Yang, S.C.J. Lee, E. Tangdiongga, F. Breyer, S. Randel, and A.M.J. Koonen, "40-Gb/s transmission over 100m graded-index plastic optical fibre based on discrete multitone modulation," Optical Fibre Communication/National Fibre Optic Engineers Conference (OFC/NFOEC), (OSA, 2009), Paper PDPD8).

All prior art existing systems were based on transmission of OOFDM signals originating from arbitrary waveform generators (AWG) using off-line signal processing-generated waveforms. At the receiver, the transmitted OOFDM signals were captured by digital storage oscilloscopes (DSO) and the captured OOFDM symbols were processed off-line to recover the received data. Such off-line signal processing approaches did not consider the limitations imposed by the precision and speed of practical DSP hardware that are required for insuring real-time transmission.

It has been improved by introducing signal modulation technique known as adaptively modulated optical OFDM (AMOOFDM), offering advantages such as:

- flexibility, robustness and optimal transmission performance;

- efficient use of spectral characteristics of transmission links; individual subcarriers within a symbol can be modified according to needs in the frequency domain ;

- use of existing multimode fibres and corresponding network;

- low installation and maintenance cost.

These have been described and discussed for example in Tang et al. (J.

Tang, P.M. Lane and K.A. Shore in I EEE Photon. Technol. Lett, 1 8, n ^Q 1 , 205- 207, 2006 and in J. Lightw. Technol., 24, n ^Q 1 , 429-441 , 2006) or in Tang and Shore (J. Tang and K.A. Shore, in J. Lightw. Technol., 24, n ^Q 6, 231 8-2327, 2006). Additional aspects such as

- the impact of signal quantisation and clipping effect related to analogue to digital conversion (ADC) and determination of optimal ADC

parameters;

- maximisation of transmission performance;

have been described in Tang and Shore (J. Tang and K.A. Shore, in J. Lightw. Technol., 25, n°-3, 787-798, 2007).

In order to implement real-time OOFDM transceivers, there is a need to develop advanced high-speed signal processing algorithms with adequate complexity.

SUMMARY OF THE INVENTION.

It is an objective of the invention to double the capacity of transmission using OOFDM transceivers. It is also an objective of the present invention to ensure input/output reconfigurability and dynamic bandwidth allocation without modifying the optical network architecture.

It is another objective of the present invention to provide colourless optical transceivers within a broad wavelength window.

It is a further objective of the present invention to provide pre-compensation of transmission link spectral distorsion without additional hardware.

In accordance with the present invention, the foregoing objectives are realised as defined in the independent claims. Preferred embodiments are defined in the dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS.

Figure 1 represents the block diagram of the AMOOFDM transmitter and receiver suitable for all OFDM-related transmission links.

Figure 2 represents a diagram of the system used to evaluate the efficiency of the inverse fast Fourier transform ( I FFT)/fast Fourier transform (FFT) logic functions in the working range of a high speed transceiver, by placing them back to back in the same field programmable gate array.

Figure 3 represents constellations of 16-QAM encoded first subcarrier.

Figure 4 represents the experimental system setup of the present invention.

Figure 5 represents the launch offset.

Figure 6 represents the bit error rate (BER) performance of 3 Gb/s DQPSK- encoded OOFDM signal transmission over a 500 m MMF and an optical back to back, as a function of optical launch power expressed in dBm. Figure 7 represents constellations of the 1 , 9 and 15 DQPSK-encoded subcarriers for 3 Gb/s signals transmitting through 500 m MMF for a BER of 3.3x10 ^"9 .

Figure 8 represents constellations of the 1 ^st , 9 ^th and 15 ^th DQPSK-encoded subcarriers for 3 Gb/s signals transmitting through 500 m MMF for a BER of 1 .8x10 ^"4 .

Figure 9 represents BER and optical launch power expressed in dBm as a function of offset expressed in micrometres.

Figure 10 represents BER performance of 3 Gb/s 16-QAM-encoded OOFDM signal transmission over a 500 m MMF and an optical back to back, as a function of reseived optical power expressed in dBm.

Figure 1 1 represents constellations of the 1 ^st , 9 ^th and 15 ^th 16-QAM-encoded subcarriers for 3 Gb/s signals transmitting through 500 m MMF for a BER of 1 .2x10 ^"9 .

Figure 12 represents constellations of the 1 ^st , 9 ^th and 15 ^th 16-QAM-encoded subcarriers for 3 Gb/s signals transmitting through 500 m MMF for a BER of 1 .88x10 ^"4 .

Figure 13 represents the signal line rate expressed in Gb/s as a function of transmission distance expressed in km

DESCRIPTION OF THE PREFERRED EMBODIMENTS.

The present invention discloses a method for increasing the transmission capacity of an optical orthogonal frequency division multiplexing (OFDM) transceiver that comprises the steps of;

a) encoding the incoming binary data sequence into serial complex numbers using different signal modulation formats; b) applying a serial to parallel converter to the encoded complex data; c) generating a sum of two individual sets of 2N parallel data, {A} and {B} wherein {A} and {B} satisfy the relationships Α ₂ Ν- _Π = A ^* _n and Β ₂ Ν- _Π = B ^* _n for n ranging from 1 to 2N-1 , A ^* and B ^* being respectively the complex conjugates of A and B, and wherein {A} and {B} also satisfy the relationships lm{A ₀ }= lm{A _N }= lm{B ₀ }= lm{B _N }= 0

d) applying the inverse of a time to frequency domain transform, to the sum of these 2 sets of sub-carriers using field programmable gate array (FPGA)-based transform logic function algorithms in order to generate parallel complex OFDM symbols wherein the k-th symbol can be expressed as

S _k ^A+B (t) = ∑ _n =o to 2N-i A _k exp(i2nnAft) + ∑ _n =o to 2N-i B _k exp(i2nnAft)

= l _{k A} (t) + iQk_ _B (t)

wherein Δί is the frequency spacing between adjacent subcarriers and wherein I and Q represent respectively the in-phase component and the quadrature component;

e) inserting a prefix in front of each symbol of step d), said prefix being a copy of the end portion of the symbol;

f) serialising these symbols in order to produce a long digital sequence; g) applying two digital to analogue converters to convert the real and

imaginary parts of the digital sequence into analogue waveforms;

h) applying an electrical to optical converter to generate an optical

waveform;

i) coupling the optical signal into a single mode fibre (SMF) or multimode fibre (MMF) or polymer optical fibre (POF) link.

said method being characterised in that, in the transmitter, two complex signals A _k and B _k are input into the inverse transform

and wherein the in-phase component of the inverse transform output contains information from A alone and the quadrature component contains information from B alone.

A schematic drawing of the transmitter/receiver system is represented in figure 1 . This is suitable for achieving transmission speeds as large as 80 Gb/s.

OFDM is a multi-carrier modulation technique wherein a single high-speed data stream is divided into a number of low-speed data streams, which are then separately modulated onto harmonically related, parallel subcarriers, said subcarriers being positioned at equally spaced frequencies. Their overlapping spectra do not interfere at the discrete subcarrier frequencies thereby resulting in high spectral efficiency. In the transmitter, the frequency domain subcarriers are transformed into time domain symbols, and in the receiver the time domain symbols are transformed back into frequency domain subcarriers. The inverse and direct transforms used respectively in the transmitter and in the receiver must be of the same nature.

The signal modulation formats are those typically used in the field and are described for example in Tang et al. (Tang J.M., Lane P.M., Shore A., in Journal of Lightwave Technology, 24, 429, 2006.). The signal modulation formats vary from differential binary phase shift keying (DBPSK), differential quadrature phase shift keying (DQPSK) and 2 ^P quadratic amplitude modulation (QAM) wherein p ranges between 3 and 8, preferably between 4 and 6. The information is thus compressed thereby allowing reduction of the bandwidth.

DQPSK signal modulation has the property that no channel estimation is necessary, as data is encoded using phase change only. To further improve the transmission capacity, the use of higher signal modulation formats such as M-ary QAM is desirable. In M-ary QAM systems, both absolute amplitude and phase values are used meaning that channel estimation is vital. Such new system characterised by high accuracy, low complexity, comparatively short overhead, no symbol buffering requirement and adaptive modulation is described for example in Giddings et al. (R. P. Giddings, X.Q. Jin, H.H. Kee, X.L. Yang and J.M. Tang, "Experimental implementation of real-time optical OFDM modems for optical access networks", European Workshop on Photonic Solutions for Wireless, Access, and ln-house Networks, May 2009, Duisburg, Germany).

The serial to parallel converter truncates the encoded complex data sequence into a large number of sets of closely and equally spaced narrow-band data, the sub-carriers, wherein each set contains the same number of sub-carriers 2N. N is equal to 2 ^P wherein p is an integer of at least 3 up to 8, preferably, it is 7. In each parallel data, the amount of information is directly proportional to the clock beat. It ranges between 50 and 256 MHz.

Discrete or fast Fourier transforms (DFT or FFT) are typically used in the field. Preferably FFT is used as it reduces significantly the computational complexity, which however remains very computationally demanding. 2 ^P point IFFT/FFT logic function is preferably used in the present invention, wherein p is an integer ranging between 5 and 8 and is preferably equal to 7. It employs a radix-2 decimation-in-time structure comprising 2-point butterfly elements as core computational building blocks. It uses a number of extensively paralleled processing stages. The computational precision at each stage of the IFFT/FFT is controlled to allow the overall calculation precision to be maximised whilst maintaining acceptable logic resource utilisation. The design is also scaled to support long transform length required for increasing the number of subcarriers, and further adapted for high clock speed necessary for increased symbol rate. Moreover, IFFT/FFT function also includes adjustable clipping and quantisation of the output samples.

It is preferable to assess the selected real-time IFFT/FFT logic functions in the working range of the high speed transceiver of the present invention. This can for example be carried out by implementing both IFFT and FFT back to back in the same field programmable gate array as shown in figure 2.

Incoming data is generated externally from a pattern generator. The single data stream is demultiplexed for input to the FPGA via high-speed deserialising transceivers. The parallel data from the transceivers is combined and fed to parallel encoders to generate complex data for input to the IFFT logic function. These parallel complex numbers and their corresponding conjugate counterparts are arranged to satisfy Hermitian symmetry. This results in the generation of real-valued time domain samples at the output of the IFFT. The output samples from the IFFT function, representing the OFDM symbol, are fed directly to the input of the FFT function. The resulting parallel data is fed to high-speed serialising transceivers. The data streams are multiplexed into a single data stream. The bit error ratio (BER) is measured with an error analyser. The IFFT/FFT algorithms used in the present invention can be operated up to 80 Gb/s.

The field-programmable gate array (FPGA) is a semiconductor device that can be configured as required by the end-user. It is programmed using a logic circuit diagram or a source code in a hardware description language (HDL) to specify how the chip will work. It is used to implement any logical function that an application-specific integrated circuit (ASIC) could perform and it further has the ability to update the functionality. It contains programmable logic components and a hierarchy of reconfigurable interconnects that allow the blocks to be "wired together". Logic blocks can be configured to perform complex combinational functions and they include memory elements. In the present invention steps a) through f) are carried out by FPGA. The FPGAs used in the present invention for real-time hardware-based digital signal processing (DSP) are commercially available.

Digital to analogue converters (DAC) are applied to both the real and imaginary parts of the digital sequence.

The analogue to digital converter (ADC) is an electronic device that converts a continuous analogue signal to a flow of digital values proportional to the magnitude of the incoming signal. Most ADC are linear, meaning that the range of the input values that map to each output value has a linear relationship with the output value. If the probability density function of a signal being digitised is uniform, the signal-to-noise ratio relative to the quantisation noise is ideal. As this is very rarely so, the signal has to be passed through its cumulative distribution function (CDF) before quantisation, thereby allowing quantisation of the most important regions with highest resolution.

ADC has several sources of errors such as:

- quantisation errors;

- clipping errors;

non-linearity;

- aperture errors due to clock jitter.

The analogue signal is continuous in time and is converted into a flow of digital values with a predetermined sampling rate. A continuously varying band limited signal can be sampled and be exactly reproduced from the discrete-time values by an interpolation formula provided the sampling rate is higher than twice the highest frequency of the signal.

Since ADC cannot make an instantaneous conversion, typical ADC integrated circuits include sample and hold subsystem internally.

All ADCs work by sampling their input at discrete intervals of time. If the input is changing slowly compared to the sampling rate, it can be safely assumed that the value of the signal between two sampling lies between the two sampled values. If, however, the input signal is changing much faster than the sample rate, aliased signals are produced at the output of the DAC. The frequency of the aliased signal is the difference between the signal frequency and the sampling rate. Aliasing can be limited by applying a low-pass antialiasing filter in order to remove all frequencies higher than the sampling rate.

ADC performance can further be improved by adding a very small amount of random noise to the input before conversion, its amplitude being set to be about half of the least significant bit.

The electrical to optical transformation is carried out with directly modulated distributed feedback (DFB) lasers which are well known in the field. The prior art optical networks such as wavelength division multiplexing passive optical networks (WDM-PONs), or intensity modulation direct detection (IMDD) require real-valued inverse transform signals. In order to satisfy such requirement, the 2N subcarriers containing the encoded signal and its complex conjugate being input to the inverse transform must be arranged to satisfy Hermitian symmetry. The consequence of such

requirement is the generation of a real valued signal as real output of the inverse transform and zero as its imaginary output, thereby wasting half the available resources. The present invention on the contrary makes use of both the real and imaginary parts of the inverse transform to carry information.

The length of the cyclic prefix copied in front of the symbol is determined in order to obtain a ratio (length of cyclic prefix)/(total length of symbol) ranging between 5% and 40%.

The optical fibres used in the present invention can be selected from single mode, multimode or polymer optical fibres.

Single mode optical fibres (SMF) are designed to carry only a single ray of light. They do not exhibit modal dispersion resulting from multiple spatial modes and thus retain the fidelity of each light pulse over long distances. They are characterised by a high bandwidth. They can span several tens of kilometers at 1 Tb/s.

Multimode optical fibres (MMF) are mostly used for communication over shorter distances. Typical multimode links have data rates of 10 Mb/s to 10 Gb/s over link lengths of up to 600 metres. They have a higher light gathering capacity than SMF but their limit on speed times distance is lower than that of SMF. They have a larger core size than SMF and can thus support more than one propagation mode. They are however limited by modal dispersion, resulting in higher pulse spreading rates than SMF thereby limiting their information transmission capacity. They are described by their core and cladding diameters. Polymer optical fibres (POF) are made of plastic such polymethylmethacrylate (PMMA) or perfluoribated polymers for the core and fluorinated polymers for the cladding. In large-diameter fibres, the core, allowing light transmission, represents 96% of the cross section. Their key feature is cost effectiveness and high resistance to bending loss.

Microstructured POF can also be used in the present invention.

The in-phase component l _A (t) and the quadrature component Q _B (t)

correspond to two Subcarrier Modulation (SCM) subcarriers of a single OFDM signal. After steps e), f) and g) described hereabove, they are transformed into two real-valued double sideband (DSB) baseband analogue SCM subcarriers, respectively A _D sBi (t) and A _D sB2(t).

The subcarrier to subcarrier interference is reduced by applying a phase-shift method based on Hilbert transform to A _D sBi (t) and A _D sB2(t) in order to generate respectively real-valued single sideband SCM subcarriers S _S sBi (t) and SssB2(t) which satisfy equations

SsSBm(t) = A _D SBm(t) . COS(U ^} _RFm t) - H [A _D SBm(t)]■ Sin(U ^} _RFm t) wherein m is 1 or 2, ojRFm is the intermediate radio frequency corresponding to subcarrier m and H [A _D sBm(t)] is the Hilbert transform of A _D sBm(t).

Intermediate frequencies _RFm can be varied independently in order to cover the whole frequency response curve for both signals.

The present invention furthers discloses a method for receiving data that has been transmitted according to the method described here-above and that comprises the steps of:

a) detecting the signal emerging from the single mode fibre (SMF) or multimode fibre (MMF) or polymer optical fibre (POF) link by a photodetector;

b) passing the detected signal through a low band-pass filter and an

analogue to digital converter; c) decoding the received signal into the original sequence using a direct transform of the same nature as the inverse transform used in the transmitter,

characterised in that the received data on sub-carrier i is given by:

Ai = ½ {[Re(A'i) + Re(A' _2N -i)]} + j [Im(A'i) - lm(A' _2N-i )]}

Bi = ½ {[Re(A'i) - Re(A' _2N-i )]} + j [Im(A'i) + lm(A' _2N-i )]}

wherein Re and Im represent respectively the real and imaginary parts and wherein A', represent the received values from the ith OOFDM subcarrier after the transform.

d) applying a parallel to serial conversion in order to transform the

subcarrier sets into retrieve an encoded data sequence;

e) decoding the serial complex sequence into outgoing binary data

sequence.

At the ouput, in step a), the transmitted optical signal is converted into an electrical signal using a photo detector.

The Double Capacity modems according to the present invention offer input/output reconfigurability. In the transmitter, the input data can be either from two independent data sources, or from a single data source, that has been split into two sets of data, {A} and {13}. The appropriate arrangement of these two sets of data at the input of the inverse transform operation, preferably an inverse fast Fourier transform (I FFT) operation, provides an in- phase (/) and a quadrature (Q) component at the output of the I FFT operation. Said components convey information only from {A} and {B}, respectively. Therefore, {A} and {B} can be recovered independently by two individual end- users in the receiver. Alternatively, these two sets of data can also be recovered simultaneously by a single end-user using a similar receiver. Coherent OOFDM, typically used in the prior art is not capable of offering the above-mentioned input/output reconfigurability, as the resulting / and Q components in the transmitter are not separable. The modems according to the present invention are used in wavelength division multiplexed passive optical networks (WDM-PONs), and provide the following technical advantages:

^■ Dynamic bandwidth allocation capability: in pure WDM-PONs, one optical carrier having a fixed bandwidth is assigned to one dedicated end- user only. Without requiring any modifications to the fibre infrastructure and by using a single optical carrier, the use of the proposed modems allows two end-users to share dynamically a total bandwidth twice as large as that corresponding to a single end-user.

^■ Doubled end-users: the use of the present modems in WDM-PON having a specific number of optical wavelengths is able to double the number of end-users without compromising the bandwidth offered to each end-user as compared to the number of end-users supported by a pure WDM-PON of the prior art.

Broadcasting functionality: one of the data sets can be utilised to carry a broadcasting signal, which is distributed to the end-user along with its own traffic carried by the other data set, instead of transmitting end-user data.

Network monitoring functionality: {A}, {B} and {A}+{B} can be recovered simultaneously and independently. The modems according to the present invention can thus be used to perform network functionalities such as network monitoring and resilience.

^■ Cost reduction: the use of the present modems in WDM-PONs brings significant cost savings as compared to that of conventional AMOOFDM- SCM schemes. This is due to the simplified modem configurations and to the double number of end-users served.

Examples- Example 1 . Evaluation of real-time IFFT/FFT logic functions at 10Gb/s.

Both the IFFT and FFT functions were implemented in the same FPGA in a back-to-back configuration, as shown in Fig. 2. 10Gb/s incoming data was generated externally from a pattern generator. This single data stream was demultiplexed into four 2.5Gb/s streams for input to the FPGA via four highspeed deserialising transceivers. The parallel data from the transceivers was combined and fed to 15 parallel 16-QAM encoders to generate complex data for input to the I FFT logic function. Subcarrier 0 corresponding to zero frequency in the electrical domain was set to zero, and the 15 encoded complex numbers filled the positive frequency bins. For these 16 subcarriers, the 16 complex conjugate counterparts were generated and positioned in the negative frequency bins in such a way that Hermitian symmetry was satisfied between them. This resulted in the generation of 32 real-valued time domain samples at the output of the I FFT as required for the generation of real-valued signals for intensity modulated and direct detection (IMDD) systems.

The output samples from the IFFT function, representing the OFDM symbol, were fed directly to the input of the FFT function, the 15 data-carrying subcarriers in the positive frequency bins were selected from the output, which were then decoded by 15 parallel 16-QAM decoders. The resulting parallel data was fed to four high-speed serialising transceivers. The four data streams at 2.5Gb/s were multiplexed to a single 10Gb/s data stream and BER was measured with an error analyser. The FPGA ran at a clock speed of 156.26MHz. The clocks for all the elements were generated with clock synthesisers using a common reference source. Zero bit error was detected by the error analyser at 10Gb/s operation. The constellation of the first subcarrier at the FFT output is shown in Fig. 3. It is typical of all subcarriers. It clearly shows that the performance of the real-time DSP is capable of supporting at least 10Gb/s OOFDM transmission.

Example 2. Real time transceiver architecture.

In the real time OOFDM transceiver architecture represented in figure 1 , a 32 point IFFT was used to support 32 subcarriers, of which 15 carried encoded real data. A parallel random data source fed 15 encoders, each of which encoded the random data using a specific signal modulation format to produce complex numbers. These 15 subcarriers, their corresponding complex conjugate counterparts and two subcarriers carrying zero power were arranged as described in example 1 in order to generate real-valued time domain samples at the output of the IFFT. The 32 signed, real-valued samples exiting the IFFT were clipped and quantised with a number of bits set to 8, in order to match the resolution of the DAC. In order to mitigate the inter- symbol interference (ISI) effect caused by modal dispersion, a cyclic prefix of 8 samples was added to each time domain symbol, giving rise to 40 samples per symbol. The internal system clock was set to be 100MHz, and the parallel processing approach resulted in a 100MHz symbol rate. The 100MHz symbol rate and 40 samples per symbol gave a sample rate of 4GS/s. The signed samples were converted to unsigned values by adding an appropriate DC offset in order to obtain all positive values as required by the DAC. After performing sample ordering and bit arrangement, the unsigned 40 samples were streamed to the DAC interface at 4GS/s. An entire symbol consisting of 320 bits was fed in parallel to 32 high speed 10:1 dedicated hardware serialisers. The interface consisted of 4 samples transferred in parallel at a rate of 1 GHz, for an aggregated sample rate of 4GS/s. The DAC generated an analogue electrical OOFDM signal having a maximum peak-to-peak voltage of 636mV. This signal was then used to modulate the data manipulation language (DML).

At the receiver, the optical-to-electrical conversion was performed using a PIN. Tthe analogue electrical signal was digitised by a 8-bit ADC operating at 4GS/s. A digital interface, identical to that of the DAC in the transmitter, transferred the digital samples at 4GS/s to the second FPGA. The 32 high speed, 1 :10, dedicated hardware deserialisers captured 40 received samples in parallel. Bit rearrangement and sample ordering was also performed to reconstruct the samples in the correct order. The samples were then converted to signed values by removing the ADC zero-level code.

Symbol alignment was vital to ensure that the 40 parallel samples captured by the deserialisers in the receiver originated from the same symbol generated in the transmitter. Symbol alignment was performed by continuous transmission of symbols of a fixed pattern over the transmission system. The sample offset was determined and subsequently compensated. Such a symbol alignment process was performed only once at the establishment of a transmission connection.

The first 8 samples of each of the captured, corresponding to the cyclic prefix inserted in the transmitter, were removed, resulting in 32 samples for input to the 32 point FFT function, which determined the phase and amplitude of each subcarrier. At the FFT output, 15 subcarriers in the positive frequency bins were selected for decoding. The recovered data bits from each symbol were analysed by a BER analyser function, said function being used to regenerate the transmitted bit pattern, synchronise it with the received pattern and continuously detect and count bit errors.

The bit errors counted over 100 million symbols were displayed with the embedded logic analyser, thereby allowing fine adjustment of the system parameters to maximise the transmission performance. In addition, the logic analyser also displayed and continuously updated the total number of bit errors and the corresponding symbols accumulated since the start of a transmission session.

Example 3. Transceiver setup

In the experimental setup represented in figure 4, the electrical signal from the DAC was attenuated in order to optimise the modulating current. It was then it employed, together with an adjustable DC bias current, to modulate a single- mode 1550nm DFB laser with a 3-dB modulation bandwidth of approximately 10GHz. The OOFDM signal from the DFB laser was coupled, via a variable optical attenuator and an optional 3D positioner, into a 500m 62.5/125μιτι MMF having a 3dB optical bandwidth of about 1200MHz-km and a linear loss of 1 dB/km. An optical attenuator was used to control the optical power launched into the MMF link.

At the receiver, the OOFDM signal was detected using a 20GHz PIN with TIA. The PIN had a receiver sensitivity of -17dBm, corresponding to 10 Gb/s nonreturn-to-zero data at a BER of ι.οχΐο ⁹ . The optical-to-electrical converted signal was first amplified with a 2.5GHz, 20dB RF amplifier, then attenuated as necessary to optimise the signal amplitude to suit the ADC's input range. This adjustment also provided electrical gain control to compensate for the variation in received optical power level. After passing through an electrical low-pass filter, the signal was converted via a balun to a differential signal and then digitised by a 4GS/s, 8-bit ADC in the receiver.

The performance robustness was examined for different offset launch conditions. The optical signal from the DFB laser was coupled into the MMF via a 3D positioner, enabling the fine adjustment of position of laser launch spot to emulate different launch offsets. The definition of the offset is represented in figure 5. As reference point, the central launch position is identified first by adjusting the position of the laser launch spot in the X and Y dimensions until the optical power received at the far end of the MMF is maximised with the corresponding offset ranges being symmetrical and maximised in both the X and Y dimensions. For the MMF adopted in the experiments, the maximum offset range without affecting significantly the output optical power was of about ±25μιτι.

Example 4. DQPSK-encoded OOFDM transmission performance.

The transmission performance of 3Gb/s DQPSK-encoded OOFDM signals was examined in an IMDD 500m MMF system involving the DML represented in figure 4. Figure 6 represents the measured BER as a function of optical launch power for optical back-to-back and for 500m MMF transmission. The FPGA operated at a clock speed of 100MHz, and the sample rates of the DAC/ADC were 4GS/s. The DFB bias current was set to 38mA. A 1 m mode conditioning patch chord was used to couple the optical signal into the MMF transmission system. It can be seen from figure 6 that, for the case of 500m MMF transmission, a BER as low as 3.3x10 ^"9 was achieved at optical launch powers of more than -9.2dBm. Error floor were not detected for both cases. Taking into account the total linear link loss of about 1 dB, an optical power penalty of approximately 3dB at a BER of 1 .0x10 ^"4 was obtained, said penalty resulting mainly from the modal noise effect as discussed by Gasulla and Capmany (J. gasulla and J. campmany, 'Modal noise impact in radio over fiber multimode fiber links.' Opt. Express, 16, 121 -126, 2008).

After transmitting through the 500m MMF, the constellations of the 1 ^st , 9 ^th and 15 ^th subcarriers are presented in figure 7 for BER of 3.3x10 ^"9 and in figure 8 for BER of 1 .8x10 ^"4 . As seen in these figures, the subcarrier amplitude decreased rapidly for subcarriers located at high frequencies.

Example 5. Performance of offset launch conditions.

Performance robustness to different offset launch conditions was examined. The transmission link configuration and the transceiver parameters were identical to those used in obtaining figure 6, except that a 3D positioner was utilised here, as shown in figure 4. For 3Gb/s transmission of DQPSK- encoded OOFDM signals over the 500m MMF, the measured BER versus launch offset is shown in figure 9, which also represents the variation of the corresponding optical launch power at the input facet of the MMF link.

Excellent performance robustness was observed for BERs of less than

1 .0x10 ^"5 being maintained over the entire launch offset range of ±25μιτι. The results imply that the adopted cyclic prefix was sufficiently long to compensate for the differential mode delay (DMD) variation induced by different launch offsets. Such performance robustness could be improved further using adaptive modulation on different subcarriers within an OOFDM symbol.

Example 6. 16-QAM-encoded OOFDM transmission performance.

The FPGAs' operating speeds and the sample rates of the DAC/ADC were set at 50MHz and 2GS/s, respectively, and a channel estimation technique was incorporated in the OOFDM transceiver design. A 3Gb/s OOFDM signal was produced with 16-QAM taken on all the 15 data-carrying subcarriers. The transmission performance of the 16-QAM-encoded 3Gb/s OOFDM signal over a transmission system identical to that represented in figure 6 allowed the evaluation of the transceiver design as well as comparison of the transmission performances of different modulation format-encoded OOFDM signals for a signal bit rate of 3Gb/s. For such transmission system scenario, the measured BER versus received optical power is represented in figure 10, wherein the DFB bias current was set to 36mA. Figure 10 shows that for received optical powers of more than -8.6 dBm, BER of less than 1 .2x10 ^"9 were measured for 500 m MMF transmission without error floor.

It was observed that for achieving a BER of 1 .0x10 ^"4 , a 3.7dB increase in optical power was required when replacing DQPSK by 16-QAM. This is in excellent agreement with theoretical predictions reported by tang and Shore (J.M. Tang and K.A. Shore, 'maximizing the transmission performance of adaptively modulated optical OFDM signals in multimode-fiber links by optimizing analog-to-digital converters.' J. Lightwave Technol., 25, 787-798, 2007). Figure 10 also shows a power penalty of approximately 2dB at a BER of 1 .0x10 ^"4 , lower than that shown in figure 7 for DQPSK. Such difference can be explained by the fact that for transmitting the 3Gb/s OOFDM signal, the transmission bandwidth required by the 16-QAM-encoded signal is halved with respect to that of the DQPSK-encoded signal. As a direct result, the roll- off effect was not as significant as that observed for DQPSK. Figures 1 1 and 12 present respectively the constellations of the 1 ^st , 9 ^th and 15 ^th subcarriers for BER of 1 .2x10 ^"9 and of 1 .88x10 ^"4 after transmitting through the 500m MMF.

Example 7. Comparison between the present system and conventional systems.

Figure 13 shows the effectiveness of the invented technique in improving the transmission performance of AMOOFDM-based transmission systems. Several cases are represented:

1 ) Conventional AMOOFDM, in which only one FPGA was involved (RS);

2) Several AS Cases, in which two FPGAs were used in order to generate two real-valued double side band (DSB) AMOOFDM signals;

3) Several RS cases in which one FPGA was used and wherein the modems are similar to those of the AS systems. In AS I, one AMOOFDM signal operated at the baseband, the other being modulated onto an intermediate RF carrier.

AS II was formed by inserting, between the optical carrier and the baseband AMOOFDM signal of AS I, a spectral gap having a width of twice of the signal bandwidth.

In AS III, single sideband (SSB) modulation in the electrical domain was applied to the two AMOOFDM signals of AS II.

Each of RS I, II and III, required a single FPGA. The general structures of the three RS modems were similar to those corresponding to the AS schemes. The only differences between these two sets of modems were the signal processing approaches used in distributing the encoded incoming data prior to the IFFT operation in the transmitter and those adopted in recovering the received data after the FFT operation in the receiver.

It was observed that AS II and III and RS II and III systems had a better signal line rate than AS I and RS I systems at distances of less than 80mkm, whereas the reverse was true for distances larger than 80 km. This is due to the fact that examples AS III and RS III need a high signal bandwidth. The frequency response narrows with increasing transmission distances and these systems are thus in an unfavourable situation for long transmission distances. They perform best on short transmission distance with wide frequency response. For long transmission distances AS I and RS I are more desirable and they happen to be cheaper than the other systems.