We demonstrate a field programmable gate array (FPGA) based optical orthogonal frequency division multiplexing (OFDM) transmitter implementing real time digital signal processing at a sample rate of 21.4 GS/s. The QPSK-OFDM signal is generated using an 8 bit, 128 point inverse fast Fourier transform (IFFT) core, performing one transform per clock cycle at a clock speed of 167.2 MHz and can be deployed with either a direct-detection or a coherent receiver. The hardware design and the main digital signal processing functions are described, and we show that the main performance limitation is due to the low (4-bit) resolution of the digital-to-analog converter (DAC) and the 8-bit resolution of the IFFT core used. We analyze the back-to-back performance of the transmitter generating an 8.36 Gb/s optical single sideband (SSB) OFDM signal using digital up-conversion, suitable for direct-detection. Additionally, we use the device to transmit 8.36 Gb/s SSB OFDM signals over 200 km of uncompensated standard single mode fiber achieving an overall BER<10−3.
©2009 Optical Society of America
Optical orthogonal frequency-division multiplexing (OFDM) has recently gained substantial interest from both the academic and industrial communities  because of its advantages which include high spectral efficiency and simple distortion equalization. Additionally, the OFDM multiband technique proposed in  can relax the speed and bandwidth requirement of the signal converters while providing finer switching granularity and more network service flexibility. The suitability of optical OFDM to convey data and services in the next generation of optical networks has been extensively investigated for both direct and coherent detection [2–7]. The two detection schemes have essentially the same transmitter design and only differ in the receiver. Direct-detection OFDM benefits from a simpler and cheaper receiver as it only requires a single photodiode and digital signal processing (DSP), but with lower sensitivity and spectral efficiency. Coherent detection, on the other hand, has a higher sensitivity and spectral efficiency, but comes with additional cost and complexity due to the requirement for a local oscillator laser and other optical components, and also a more complex DSP for phase and polarization tracking. Some of the DSP complexity may be reduced by using a self-coherent OFDM receiver . In the coherent configuration (CO-OFDM), data rates over 100 Gb/s have been demonstrated over hundreds of kilometers of uncompensated fiber [2,3]. Similarly linear and nonlinear tolerance for direct-detection OFDM has been extensively studied and experimentally verified [5–7]. Recently 108 Gb/s DD-OFDM transmission has been demonstrated over 20 km of standard single-mode fiber (SSMF) using polarization multiplexing . In addition to telecom applications, optical OFDM is also ideally suited to provide 40 and 100 Gb/s Ethernet services for data centers and local area networks deploying multimode fiber [10,11].
The abovementioned progress in optical OFDM range, data throughput and resilience has been demonstrated using arbitrary waveform generators at the transmitter and fast sampling oscilloscopes at the receiver coupled with offline processing at both the transmitter and the receiver. In order to go one step further towards deploying optical OFDM in real systems and to confirm its viability, it is necessary to verify the developed techniques and algorithms with real-time transceivers. Since OFDM is a primarily digital technique, its adoption at optical communications line-rates has been dictated by the speed of DSP and signal converters, namely digital-to-analog (DAC) and analog-to-digital (ADC) converters. Recently, multi-gigabit per second DACs and ADCs have become commercially available making possible the real-time implementation of optical OFDM. Moreover, the DSP can be implemented at high speeds using field programmable gate arrays (FPGA) which offer cost-effectiveness and flexibility for experimental work. A real-time coherent optical OFDM receiver has been reported recently in . The FPGA-based device operates at a sample rate of 1.4 GS/s, allowing the detection of data rates up to 3.1 Gb/s. However, to the best of our knowledge, no multi-gigabit per second OFDM transmitter has been reported to date.
In this paper, we report the first real-time OFDM transmitter capable of operating at multi-gigabit optical line rates. It operates at a sample rate of 21.4 GS/s, and the goal of this work is to generate signals at data-rates up to 33 Gb/s using quadrature phase shift keying (QPSK). The format used is only limited by the resolutions of the DAC (4-bit) and the IFFT core (8-bit), and the design could be easily extended to higher order quadrature amplitude modulation (QAM) format. The transmitter uses an optical modulator, but could be adapted to use a directly modulated laser, and can be either coherently or directly detected. In the following sections, the design and performance of the real-time transmitter are discussed. Section 2 explains the OFDM DSP architecture, including the inverse fast Fourier transform (IFFT) core, clipping and choice of oversampling rate. The performance of the transmitter generating an electrical 8.36 Gb/s OFDM signal, suitable for driving an optical modulator, is then investigated. Finally, in section 3 we demonstrate 8.36 Gb/s optical SSB OFDM signal generation and transmission with direct-detection over 200 km of uncompensated standard SMF, with an overall BER < 10−3.
2. Transmitter design
An optical OFDM transmitter can be considered to be a “universal” transmitter because it can be adapted to different fiber types (single mode or multimode), different network ranges (short or long-haul) and different detection techniques (direct or coherent) while providing bit-rate flexibility in terms of modulation depth and utilized bandwidth. A conceptualized optical OFDM transmitter diagram is shown in Fig. 1 (dashed boxes relate to optional steps).
The transmitter can be divided into three distinct parts: digital signal processing (DSP), analog frontend and an optical part. In the DSP part, the binary data stream may be first pre-coded (e.g. forward error correction, FEC) then mapped onto a quadrature amplitude modulation (QAM) constellation. After this, the data is sent to an IFFT module, following which a cyclic prefix may be added to each OFDM symbol to mitigate dispersion. A pre-equalization stage may be necessary to compensate for the frequency roll-off introduced by the DAC. This step can also be used to compensate for any imperfections in the analog section. Finally, a clipping module is used to adjust the peak to average power ratio (PAPR) in order to optimize the DAC’s performance and reduce the effects of optical nonlinearities. Other PAPR reduction techniques may also be used before the IFFT block, such as coding and phase scrambling. In the analog part, a low-pass filter (LPF) is used to remove any OFDM band image introduced by the DAC. Electrical I/Q mixers may be used to shift the OFDM band to a desired intermediate RF frequency. This technique has the advantage of allowing multi sub-band multiplexing and also full DAC bandwidth utilization in direct-detection systems [2,4]. Alternatively, a RF tone can be inserted to create a virtual carrier and improve the bandwidth utilization of the DAC . Because the DAC is the interface between the DSP and the analog domain, its parameters such as speed, resolution, effective number of bits (ENOB), define the DSP configuration and thus the performance of the entire system as will be discussed in the next section. Finally the interface to the optical section consists of either an external modulator or a directly modulated laser (DML). Optical I/Q mixing can also be used in tandem or as an alternative to electrical mixing . An optical filter may be deployed for single sideband OFDM generation, which results, in the case of direct detection, in the optical phase distortion being mapped onto electrical phase at the receiver, which can then be compensated by electronic phase equalization . This would not be possible with a double sideband signal due to destructive interference between the sidebands resulting in channel fading.
Figure 2a shows the FPGA-based optical OFDM transmitter top level design. The hardware and FPGA design used in this work for generating 21.4 GSample/s signals is based on previous work involving the real time implementation of electronic predistortion (EPD) with NRZ-OOK signals, full details of which can be found in [15,16]. The DSP was performed on a Xilinx Virtex-4 (4VFX100) FPGA which was interfaced to a 21.4 GS/s, 4-bit resolution DAC constructed from discrete components (4:1 time division multiplexers, attenuators and a combiner) as described in [15,16]. The interface between the FPGA and DAC consisted of sixteen serial lines operating at 5.35 Gb/s. The sixteen signals consisted of four groups of four. The first group contained the most significant bits of the required DAC output, the next group contained the next most significant bits etc. For each group, 4:1 time division multiplexers were used within the DAC to generate signals at the output rate of 21.4 Gb/s. The 5.35 Gb/s signals were generated using the multi-gigabit transceivers (MGT) on the FPGA. The MGT outputs were time aligned using digital delay circuits on the FPGA and external microwave phase shifters . The analog front-end consisted of an amplifier, a Bessel low pass filter with a cut off frequency of 7.5 GHz (a synchronous digital hierarchy (SDH) filter) and a bias. Electrical I/Q mixing was not considered in this work. The amplifier output bias and gain were adjusted to optimize transmission performance before applying the signal to the Mach-Zehnder modulator (MZM). An optical bandpass filter with 15 GHz passband was used following the MZM to generate the single sideband optical ODFM signal.
FPGA design: The FPGA functions are shown in Fig. 2b. All functions were controlled using a 167.2 MHz clock. The bit pattern to be transmitted was stored in a read only memory (ROM) on the FPGA and a block of N bits was read out each clock cycle. The choice of N is discussed in the section below on oversampling. The N-bits were modulated to form N/2 complex values representing the input QPSK constellations to the 128 point IFFT core. In each clock cycle, the IFFT core generated 128 complex outputs, each with 8-bit resolution. In this case, only the real values were used which were clipped and converted to 4-bit words for the DAC. The clipping circuits operate in an identical way to the scaling circuits used in the EPD work [15,16] and the clipping factors (minimum/maximum amplitude and scaling) could be updated during operation. The resulting 128 4-bit words were rearranged to 16 32-bit words for output by the MGTs and appropriately delayed for alignment purposes.
IFFT core: The 128 point IFFT core required for the OFDM transmitter had to support a throughput of one transform per clock cycle in order to meet the system’s goals. However, commercially available IP cores typically exhibit only a fraction of this performance. For example, the fastest 128 point IFFT core in the Xilinx LogiCore library has a throughput of one transform per 128 clock cycles. In order to reach the desired throughput, we utilized Spiral [17,18], a tool that can automatically generate hardware and software cores for DSP transforms such as the IFFT. Spiral generates designs directly from a high-level mathematical description. In doing so, it can efficiently restructure algorithms at a high abstraction level and explore choices for optimization to meet user-specified area/performance tradeoffs. In particular, Spiral can generate high throughput cores for performance demanding applications such as multi-gigabit per second OFDM signal generation.
We used Spiral to generate the 128 point IFFT core deployed on the FPGA. The core’s input and output vectors consisted of 128 complex data words, which were input and output in parallel (all 128 at once). Each data word consisted of real and imaginary parts, each in an 8 bit two’s complement fixed point format. The IFFT core had a latency of 18 clock cycles, but was fully streaming, meaning it could accept a new input vector (and produce a new output vector) on each cycle. Since the core was clocked at 167.2 MHz, its latency was thus 107.6ns, and its throughput was 21.4 GS/s. The IFFT core required approximately 65% of the FPGA’s slices (reconfigurable logic elements), and all 160 of the Virtex-4’s embedded arithmetic units (DSP48 slices).
3. Transmitter characterization
In this section, the operation of the DSP and analog front-end of the transmitter was experimentally studied. A bit sequence comprising a 215 DeBruijn pattern and synchronization overhead were loaded onto the FPGA ROM and the output of the analog front-end was measured with a 50 GS/s, 8-bit resolution real-time sampling oscilloscope (electrical back-to-back measurements). The generated signals were demodulated by offline DSP using an ideal receiver model implemented in Matlab with a true 64-bit floating point FFT. Synchronization was carried out by sending two consecutive OFDM symbols carrying identical known data (training symbols). The two symbols were then correlated at the receiver to achieve synchronization. The quality of the signals was assessed from the resulting constellations through the use of the error vector magnitude (EVM) which is a measure of distances between the ideal constellation and the symbol positions, normalized to the peak constellation symbol magnitude .
Oversampling and channel allocation: The OFDM transmitter design allows up to 128 sub-carriers, each with 167.2 MHz bandwidth giving a total bandwidth of 21.4 GHz. However, not all of this available bandwidth could be used because of the need for oversampling. This is due to the fact that the digital-to-analog converter generates the signal with a zero-order hold characteristic, creating an image (a mirror copy of the baseband) above the Nyqist frequency, Fs/2 (where Fs is the sampling frequency, 21.4 GHz). The frequency spacing between the sub-channels and the image is dependent on the oversampling rate. Figure 3a shows the DAC’s output spectrum (obtained by taking the Fourier transform of the measured time domain waveform) when generating a 10.7 Gb/s OFDM signal, carrying a 215 DeBruijn bit sequence, with sub-channels over the frequency range 5.35 – 10.7 GHz, using digital upconversion and no oversampling. This was generated by setting IFFT inputs 1:32 to zero (to form a 0 – 5.35 GHz guard band) and feeding N = 32 data channels to inputs 33:64. The negative frequencies (IFFT inputs 65:128) were all set to zero. It can be seen that the image is closely spaced to the wanted OFDM band, and cannot be removed using a practical analog lowpass filter at the output of the DAC. In the case of direct (square law) detection, the image band may beat with the main OFDM band leading to inter-channel interference. One method to overcome this issue is to slightly increase the sampling rate of the DAC. An alternative solution is to use virtual subcarriers, by setting a number of the high frequency channels to zero (corresponding to inputs to the middle ports of the IFFT core). In this work, we chose the number of virtual subcarriers to be 28 resulting in 1.28 times oversampling. Figure 3b shows the electrical spectrum of an 8.36 Gb/s SSB OFDM signal with 1.28 oversampling. This was generated by feeding N = 25 data inputs to ports 26:50 of the IFFT core, resulting in a data band between 4.18 and 8.36 GHz, while setting all other inputs to zero. Inputs 51:64 are the virtual subcarriers, while 1:25 create a guard band between 0 and 4.18 GHz set according to the principles explained in . This guard band ensures no second order intermodulation products, from the nonlinear mixing of pairs of OFDM sub-channels due to the square-law detector, fall on the used subcarrier frequencies.
It can be observed that the OFDM band and the image are 4.7 GHz apart which permits the use of a practical analog lowpass (smoothing) filter. Figure 3c shows the spectrum after a 7.5 GHz Bessel filter (an SDH filter) was placed at the output of the DAC, suppressing the image. The number of subcarriers that can be used to carry data, N, depends not only on the oversampling rate but also on the type of receiver used (i.e. coherent or direct-detection) and the configuration of the analog/optical front-end (I/Q mixing). In a digitally generated SSB direct-detection OFDM, only a quarter of the effective bandwidth can be used to transmit data . The full bandwidth can be used however in the case of coherent detection or using analog upconversion at the output of the DAC for direct-detection OFDM. In this case, the FPGA design could be used to generate a 33.4 Gb/s QPSK-OFDM baseband. Additionally, a 16.7 Gb/s discrete multi-tone (DMT) modulation can also be generated by using the complex conjugate of the data in the lower sideband . In this work, only single sideband OFDM with digital upconversion was considered. Also, pre-equalization to compensate for the DAC amplitude roll-off with frequency (which can be observed in Fig. 3) was not implemented in the transmitter, and will be developed in future work.
IFFT resolution: In Figs. 3a-c unwanted frequency components can be seen in the 0 – 4.18 GHz guard band. To investigate the cause of this, we simulated the operation of the transmitter with a range of IFFT resolutions. Figures 3d-f show the simulated transmitter spectra using 8, 12 and 16-bit resolution IFFT cores respectively. They were obtained by generating the hardware description (VHDL) of the DSP section using Spiral and modeling its output using ModelSim. The ModelSim results were then fed to a Matlab module that simulates the response of the 4-bit DAC and a 7.5 GHz 5th order Bessel filter (as used in the experimental setup). Similar to the experimental spectra, the unwanted frequency components in the 0 – 4.18 GHz band can be observed in Fig. 3d (8-bit IFFT). As the IFFT resolution is increased to 12-bit, only residual tones are observed around DC (Fig. 3e) and become negligible using a 16-bit core (Fig. 3f). The IFFT core contains 7 stages of multiplications/additions (log2(IFFT size)) and at each stage the data is truncated leading to a slight decrease in the precision. The loss of precision is more acute for lower resolution arithmetic leading to larger output errors and this explains the appearance of unwanted tones in the 8-bit case and to a lesser extent the 12-bit IFFT. Our choice of 8-bit IFFT resolution is purely due to memory constraints of the hardware and further investigation is required to determine the optimum trade off between precision and complexity.
Clipping: The clipping function on the FPGA was used to optimize the quality of the signal. Figure 4a shows the effect of changing the clipping ratio on the error vector magnitude (EVM) for different DAC effective numbers of bits obtained using numerical simulation. This consisted of measuring the quality of an OFDM signal generated using true FFT/IFFT (64-bit floating point) modules, a clipping circuit and a noiseless zero-order holding DAC (ADC noise was not included in the simulation). The relationship between EVM and BER for different modulation formats is presented in  and is shown in Fig. 5b where an EVM of −9.8 dB for a QPSK system is equivalent to a BER of 10−3. The clipping ratio is defined as the maximum permissible amplitude divided by the average input power of the OFDM signal . It can be observed that the optimum clipping ratio that results in the minimum EVM increases linearly with increasing effective number of bits of resolution. It is 4.5 dB for a 3-bit ENOB and increases by approximately 1 dB for every additional bit of resolution. The DAC utilized in our transmitter had a 4-bit resolution and its effective resolution was approximately 3.4 bits. Figures 4b and c show the obtained constellations without clipping and with 4.5 dB clipping ratio respectively. We found experimentally that the latter ratio gives the best EVM performance, which is in good agreement with the theoretical results of Fig. 4a.
As can be observed in the OFDM spectra of Fig. 3, the amplitude of the subcarriers follows a waterfall curve due to the DAC roll-off and the smoothing filter frequency response. This decrease in magnitude is reflected in the skewed shape of the constellations. This is illustrated in Fig. 4d where the difference in constellation amplitude between the lowest frequency (crosses) and the highest frequency (dots) channels can be clearly seen. With ASE noise, this difference in amplitude leads to a different SNR between the subcarriers and therefore the performance of the transmitter would be improved by pre-equalizing for the roll-off, although this was not implemented in this work. Figure 4e shows the post-equalized constellation of the system, using offline processing of the measured signal. The EVM per channel is plotted in Fig. 5a. It can be seen that the EVM increases with increasing channel frequency due to the DAC’s roll-off. Using Fig. 5b, the EVM values correspond to BER values ranging from <10−12 for the best channels to <10−6 for the worst channels. Figure 4a shows that by using a 6-bit resolution DAC, the EVM can be decreased by more than 10 dB and therefore the overall signal quality could be significantly improved.
4. Optical transmission
The real-time transmitter was used to generate an 8.36 Gb/s SSB optical OFDM signal for direct detection. The experimental setup is shown in Fig. 6a . 25 channels over a 4.18 GHz band (4.18 - 8.36 GHz) were used to transmit data. The 215 DeBruijn sequence and training symbols to be transmitted were loaded onto the FPGA ROM and the analog output from the DAC was amplified and then fed to the input of a Mach-Zehnder modulator. The optical signal at the output of the modulator (~-16 dBm) was boosted using an EDFA and fed to a 15 GHz optical band-pass filter to remove the lower wavelength sideband. The back-to-back OSNR was approximately 36dB (0.1 nm resolution bandwidth). The inset in Fig. 6a shows the optical spectrum after the filter (0.01nm resolution). The EVM against OSNR of the transmitter was measured in the optical back-to-back configuration using noise loading (with ASE noise from an EDFA) and is shown in Fig. 7a .
The signal was then transmitted over two 80 km spans and one 40 km span of SMF resulting in a total distance of 200 km of uncompensated standard fiber. The launch power into each span was set at −5 dBm. The signal was finally detected using a single photodiode followed by a 50 GS/s digital sampling scope. The OSNR and power at the receiver were 22 dB and 0 dBm respectively and the same ideal receiver model as before was used. No cyclic prefix was implemented in this experiment and dispersion equalization was performed off-line at the receiver. Figure 6b shows the constellation of the detected signal after the optical filter (optical back-to-back configuration) whereas Fig. 6c and 6d show the unequalized and equalized constellations after 200 km respectively. The circle markers show the average EVM across all 25 sub-channels where it can be observed that an EVM of −9.8 dB (BER = 10−3) was measured for an OSNR of 22 dB. The dashed and the solid lines represent the theoretical curves for a 3 and 4-bit DAC respectively. These curves were generated by modeling an 8-bit IFFT core and a DAC with no frequency roll-off where all the sub-channels had approximately the same EVM. The average EVM of the system is higher than the theoretical one because of the difference in quality between the higher and lower frequency sub-channels (due to the DAC’s response). However there is a good agreement between the theory and the EVM of the first channel (triangles) and we expect the EVM of the system to fall within the same range should a pre-equalization stage be deployed. Figure 7b shows the EVM value for each sub-channel for electrical back-to-back (output of the DAC connected directly to the sampling scope), optical back-to-back and after transmission over 200 km. It can be observed that the EVM penalty between the electrical and optical back-to-back configurations was only 0.5 dB.
It can also be observed that the EVM penalty after transmission compared with the optical back-to-back was 4.5 dB. This penalty is mainly due to the degradation in the OSNR and it is in good agreement with the back-to-back measurement of Fig. 7a showing that link dispersion had negligible effects on the EVM. The BER of the system was measured using offline error counting and was found to be 7.3 × 10−4. This relatively high BER at an OSNR of 22 dB is mainly explained by the back-to-back quality of the signal due to the low resolution of the DAC and IFFT core deployed and the roll-off of the DAC. This could be significantly improved by increasing the resolutions and equalizing the DAC response.
In this work, we generated 8.36 Gb/s single sideband QPSK-OFDM signals using 21.4 GS/s real-time DSP. In order to reach 10.7 Gb/s using the same technique, the sampling rate will have to be increased to at least 25 GS/s. Therefore the use of analog/optical IQ mixing or a virtual carrier would be more advantageous to exploit the full bandwidth of the DAC. Additionally, the effective bandwidth of the transmitter can be slightly increased by reducing the oversampling rate. For instance a 1.2 oversampling can produce a 35.7 Gb/s QPSK baseband. However this necessitates a sharper low pass smoothing filter to eliminate the replica band generated by the DAC. The amplitude of the higher frequency channels may be reduced even more in this case and a stronger pre-emphasis will be required. This in turn will affect the effective resolution of the DAC. Therefore the oversampling rate in OFDM systems is indirectly determined by the effective resolution of the DAC. Moreover, the DAC also dictates the modulation depth that can be generated. In our case, an approximately 3.4 effective number of bits represents the minimum resolution required to generate a QPSK constellation. The DSP on the FPGA can be easily updated to generate a QAM-16 signal using a 6-bit DAC, using hardware similar to that described in . It can be observed from Fig. 4a that the quality of the signal can be significantly increased by going to a 5 or 6-bit DAC. It also shows that the optimum clipping ratio depends on the DAC resolution. From our simulations we found that the number of subcarriers, in systems with 3 to 6 effective number of bits, has negligible effect on the optimum clipping ratio and the latter remains mainly determined by the DAC resolution. The cyclic prefix and the pre-equalization modules were not implemented in this work and will be developed in future work. Furthermore, we utilized 8-bit IFFT cores because of the limited memory size on the FPGA. Further work needs to be carried out to determine the effect on the system performance of varying the IFFT resolution.
In this paper we demonstrated a 21.4GS/s FPGA-based real-time OFDM transmitter. The DSP part consisted of an 8 bit, 128-input IFFT core, a clipping module and a 4-bit DAC. Using 1.28 oversampling, the device had a 16.7 GHz effective bandwidth, and was designed to generate signals at data rates of up to 33.4 Gb/s using QPSK-OFDM modulation. Back-to-back measurements of the transmitter found that the higher frequency channels suffered from higher BER because of the characteristics of the DAC used. These results could be significantly improved by using a higher resolution DAC and by pre-equalizing its amplitude roll-off at higher frequencies. The transmitter was used to digitally generate an 8.36 Gb/s optical single sideband QPSK-OFDM signal with 25 subchannels, suitable for direct-detection, which was transmitted over 200 km of uncompensated standard single mode fiber achieving an overall BER better than 10−3.
The authors would like to acknowledge the financial support of Intel Corporation and the UK Engineering and Physical Sciences Research Council (grant EP/C523865/1). Philip Watts would like to acknowledge financial support from the Royal Commission for the Exhibition of 1851.
References and links
1. S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, ‘Optical OFDM, a hype or is it for real?’, in Proc. Europ. Conference on Optical Comm. (ECOC), paper Mo.3.E.3 (2008)
2. W. Shieh, Q. Yang, and Y. Ma, “107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing,” Opt. Express 16(9), 6378–6386 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6378. [CrossRef] [PubMed]
3. S. L. Jansen, A. Al Amin, H. Takahashi, I. Morita, and H. Tanaka, “132.2-Gb/s PDM-8QAM-OFDM transmission at 4-b/s/Hz spectral efficiency,” Photon. Technol. Lett. 21(12), 802–804 (2009). [CrossRef]
4. A. J. Lowery, L. B. Du, and J. Armstrong,“Armstrong, ‘Performance of optical OFDM in ultralong-haul WDM lightwave systems’,” J. Lightwave Technol. 25(1), 131–138 (2007). [CrossRef]
5. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26(1), 196–203 (2008). [CrossRef]
6. Y. Benlachtar, G. Gavioli, V. Mikhailov, and R. I. Killey, “Experimental investigation of SPM in long-haul direct-detection OFDM systems,” Opt. Express 16(20), 15477–15482 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15477. [CrossRef] [PubMed]
7. Y. Benlachtar, R.I. Killey,'Investigation of 11.1Gbit/s direct-detection OFDM QAM-16 transmission over 1600km of uncompensated fiber', in Proc. Optical Fiber Comm. (OFC), paper OWM5 (2009).
8. B. J. C. Schmidt, Z. Zan, L. B. Du, A.J. Lowery, ‘100Gbit/s transmission using single-band direct-detection optical OFDM’, in Proc. Optical Fiber Comm.(OFC), paper PDPC3 (2009).
9. D. Qian, N. Cvijetic, J. Hu, T. Wang, ‘108 Gb/s OFDMA-PON with polarization multiplexing and direct-detection’, in Proc. Optical Fiber Comm.(OFC), paper PDPD5 (2009).
10. H. Yang, S. C. J. Lee, E. Tangdiongga, F. Breyer, S. Randel, A. M. J. Koonen, ‘40 Gb/s transmission over 100m graded-index plastic optical fiber based on discrete multitone modulation’, in Proc. Optical Fiber Comm.(OFC), paper PDPD8 (2009).
11. J. M. Tang, P. M. Lane, and K. A. Shore, “High-speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightwave Technol. 24(1), 429–441 (2006). [CrossRef]
12. Q. Yang, S. Chen, Y. Ma, and W. Shieh, “Real-time reception of multi-gigabit coherent optical OFDM signals,” Opt. Express 17(10), 7985–7992 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-7985. [CrossRef] [PubMed]
13. B. J. C. Schmidt, A. J. Lowery, L. B. Du, 'Low sample rate transmitter for direct-detection optical OFDM', in Proc. Optical Fiber Comm.(OFC), paper OWM4 (2009).
14. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009). [CrossRef]
15. P. M. Watts, R. Waegemans, Y. Benlachtar, V. Mikhailov, P. Bayvel, and R. I. Killey, “10.7 Gb/s transmission over 1200 km of standard single-mode fiber by electronic predistortion using FPGA-based real-time digital signal processing,” Opt. Express 16(16), 12171–12180 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-12171. [CrossRef] [PubMed]
16. P. Watts, R. Waegemans, M. Glick, P. Bayvel, and R. Killey, “An FPGA-based optical transmitter design using real-time DSP for advanced signal formats and electronic predistortion,” J. Lightwave Technol. 25(10), 3089–3099 (2007). [CrossRef]
17. P. A. Milder, F. Franchetti, J. C. Hoe, and M. Püschel, ‘Formal datapath representation and manipulation for implementing DSP transforms’, in Proc. Design Automation Conference (DAC), 385–390 (2008)
18. G. Nordin, P. A. Milder, J. C. Hoe, and M. Püschel, ‘Automatic generation of customized discrete Fourier transform IPs’ in Proc. Design Automation Conference (DAC), 471–474 (2005)
19. R.A. Shafik, S. Rahman, A.H.M. Razibul Islam, 'On the extended relationships among EVM, BER and SNR as performance metrics', in Proc. Int. Conf. on Elec. and Computer Eng.(ICECE), 408 - 411 (2006).
20. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14(6), 2079–2084 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2079. [CrossRef] [PubMed]
21. H. Ochiai and H. Imai, “Performance analysis of deliberately clipped OFDM signals,” IEEE Trans. Commun. 50(1), 89–101 (2002). [CrossRef]
22. R. Waegemans, S. Herbst, L. Holbein, P. Watts, P. Bayvel, C. Fürst, and R. I. Killey, “10.7 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation,” Opt. Express 17(10), 8630–8640 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8630. [CrossRef] [PubMed]