Back-to-Back Performance Improvement through ISI Equalization and

For an SNR of 30 dB, Dphase is 5.44 dB, which is quite significant if the phase noise is left uncompensated.

The frequency response measurement setup is also the same by replacing the PPG with a microwave synthesizer at the input of the IF amplifier. The frequency of the output signal from the microwave synthesizer is changed from 50 MHz to 1250 MHz with a step of 50 MHz and the microwave synthesizer output power was used as a reference. The received sample of this single-frequency IF signal is then digitally I/Q down-converted, low pass filtered, and Fourier transformed by the offline processor, and the results are shown as the dotted line in Fig. 2.11. Note that the resultant power was calculated and normalized to the transmitted power at the corresponding frequency, and was the average measured results of I- and Q- channels (note that there is no significant difference between the I- and Q- channels). An ideal raised cosine filter with a roll-off factor of 1 is also shown in Fig. 2.11 for comparison. The non-ideal frequency response would induce ISI on the QAM signal, and its effect was investigated through simulations by comparing the measured frequency responses with and without an equalizer (whose design will be described later). A low-pass equivalent model was used. The simulation results are shown as the solid line in Fig.

2.12. It is shown that, for SNR = 30 dB (and therefore the system is not limited by SNR), the MER penalty due to ISI is ~4.6 (=30-25.4) dB without the equalizer. The MER is limited to ~ 27 dB even with SNR > 35 dB without the equalizer because the ISI dominates the MER penalty.

2.5.2 Back-to-Back Performance Improvement through ISI Equalization and Phase Tracking

In order to improve the back-to-back MER performance, we implemented a time-domain ISI equalizer and a phase tracking block, both within a Matlab-based demodulator, as is shown in Fig. 2.13. The detailed functions of the phase tracking block and ISI equalizer are described in the following sections.

ISI Equalization: The equalizer is designed to compensate the imperfect frequency response of the back-to-back system, and is not attempted to equalize the transmission-induced transfer function.

To compensate the ISI effect in the back-to-back system, an adaptive feed-forward equalizer (FFE) is applied to equalize the system response. The adaptive equalizer is based on the well-known least-mean-square (LMS) algorithm [34]. The equalizer has 128 taps with tap frequency equivalent to symbol rate, and is trained with the collected samples in a personal computer iteratively. With ~ 10⁵ training symbols, the MER is converged and the filter coefficients are fixed in our experiment. It should be noted that the adaptive algorithm is only used to blindly compensate the static system transfer function; after the filter coefficients are converged we did not attempt to dynamically adjust it. The effect of the equalizer is illustrated in Fig. 2.12.

We can see that there was ~2.7 dB MER improvement at SNR=30 dB by using the equalizer.

Phase error correction: We used feed-forward decision directed (FF-DD) carrier phase recovery algorithm [35] for phase error correction. It has been shown that such algorithm realizes maximum-likelihood (ML) carrier phase estimation in an approximate form for high SNR. Unlike the traditional phase-locked loop (PLL) approach [21][33], the feed-forward algorithm estimate the carrier phase directly through an explicit form without relying on one-dimension searching process iteratively provided by PLL. Hence, no loop delay is introduced which is very suitable for tracking the carrier phase generated by the beating of optical carriers, such as in coherent optical systems [31], and the DSP causes negligible processing latency.

The FF-DD algorithm estimates the carrier phase for the k-th block of symbols with the following form: the complex conjugate of the i-th decision output of the k-th block of symbols derived from θ^ˆ_k−1, z_k(i) is the i-th received symbol of the k-th block, and N is the length of the block. The initial phase (θ^ˆ₀) would be estimated from the preamble bits in the acquisition stage of the phase recovery block. The decision on the i-th symbol of the k-th block is then updated after subtracting the carrier phase drift derived from the k-th ML phase estimation:

)

where a~_k(i) is the final decision output, and DEC() computes the decision metrics for M-QAM signals. It should be noted that the phase drift should not vary significantly over NT, where N is the block length and T is the symbol rate, in order to get a correct estimate. Note that a larger N can reduce the estimation error because the noise level is averaged over a larger time window, while a smaller N provides faster tracking of the carrier phase.

The resultant MER improvement due to the combined effect of ISI equalizer and phase error correction block is shown in Fig. 2.14. The case for MER improvement through only phase tracking block is shown with a dotted line for N = 125 and 25, respectively. The difference of MER between N = 125 and 25 is not significant (The measured MER at Pr = -15 dBm was 21.44 dB for N = 125, and 21.78 dB for N = 25).

Note that higher N is preferred from the viewpoint of phase updating rate even though the required buffer size is larger; for example, in our experiment, N = 25 stands for a phase updating rate of 50 MHz for 1.25Gsps symbol rate, and stands for 10 MHz for N = 125. The later significantly simplifies the hardware implementation with a reduced clock rate of the digital signal processor with negligible MER penalty. As shown in Fig. 2.14, experimentally we obtained ~ 1 dB MER improvement through the phase tracking block.

The MER performance with both phase tracking block and ISI equalizer is shown in Fig.2.14 for N = 125 and N = 25, respectively. The measured MER is 24.15 dB and 24.62 dB for N = 125 and N = 25, respectively, for Pr = -15 dBm. The total MER improvement is ~ 3.5 dB for N = 125, and ~ 4 dB for N = 25 through the combination of phase correction and ISI equalization. The equalizer by itself improves the measured MER with ~ 2.7 dB, independent of N. This improvement is consistent with the simulation result. The measured signal constellation after the phase estimation block and the equalizer is shown in Fig. 2.15(a) and 2.15(b), for N = 125 and 25, respectively.

When ISI equalization and phase error tracking are both applied, the required received optical power before the optical amplifier is ~ -28 dBm to achieve BER=10^-9 (MER=22.5 dB), according to Fig. 6.4. This received power level corresponds to ~ 2465 photons/bit for 5Gbps data rate, and the penalty is 11.4 dB compared to the ASE-limited receiver sensitivity of 178 photons/bit.

In summary, the performance improvement (at Pr = -15 dBm) through DSP blocks is shown in the following table:

The DSP blocks are then applied to the stored data for unrepeated 100 km transmission experiment and the performance is compared with results obtained from a computer simulation using VPI. The simulation parameters of VPI were the same as the parameters used in the experiment: Optical fiber loss = 0.2dB/km, optical fiber chromatic dispersion = 17ps/nm, optical fiber nonlinear index = 2.6×10^-20 m²/w, and optical fiber core area =80 μm², fLO – fQAM = 20 GHz, optical amplifier noise figure = 6 dB, modulation index = 0.6, and the symbol length = 1024×16 symbols. The MER was obtained with the combined use of VPI and Matlab. In the simulation, both the carrier phase recovery and frequency-response are assumed to be ideal, and only the fiber dispersion and nonlinear effects were considered. The simulation and experimental results (with DSP and N=125) for the 100km system are shown in Fig.

2.16. Also shown in Fig. 2.16 is the back-to-back experimental performance after DSP improvement. The measured back-to-back MER was ~24 dB, which is ~4 dB improvement from the original back-to-back MER performance of 20 dB (shown in Fig. 2.10). The improvement, as mentioned previously, was due to ~2.7 dB from ISI equalizer and ~1 dB from phase error correction. However, comparing with the theoretical calculated MER = 31 dB at Pr= -15 dBm (see Fig. 2.10), there is still a MER penalty of ~7 dB (for N=125). The ~7 dB penalty was due to the non-ideal matched filter, ADC, frequency response, and the nonideal 4-PAM electrical signal generation (as can be observed in Fig. 2.5).

.

In Fig. 2.16, the measured MER after phase error correction and ISI equalization for the 100km transmission system, at an optimum fiber input power of 2 dBm, is 23.98 dB. This is about 2 dB lower than the simulation result. For higher and

lower launched power levels than 2 dBm, the discrepancy between the measured and simulated MER is smaller, because in those power regions the nonlinear and ASE noise effects dominates over the ISI effect, respectively. Note that the reason why the measured MER is lower than the simulated ones by ~2 dB is because of the residual back-to-back penalty that could not be compensated by the DSP blocks.

The measured constellations for a launched power of 2 dBm is essentially the same as that shown in Fig. 2.15(a). At a launched power of –9 dBm and 10 dBm, the constellation diagrams of the received signal after DSP are shown in Fig. 2.17(a) and (b), respectively. In Fig. 2.17(a), we can see that the noise is higher for the constellation points at the corners, which demonstrates the modulation amplitude-dependent noise due to Sig-Sp beat noise. In Fig. 2.17(b), there is an obvious phase rotation due to self-phase modulation (SPM) for constellation points at the edges. The phase tracking algorithm could not track the constellation well when the phase shift of the constellation points is intensity dependent.

Fig. 2.1 QAM-Remote Heterodyne (QAM-RSH) transmitter configuration for the generation of a wideband optical QAM signal. BB Signal_ I/Q: Baseband in-phase/quadratic-phase component of the QAM signal. DC: constant bias voltage.

FBG: fiber Bragg grating. FPF: Fabry-Perot filter.

Fig. 2.2 System configuration for a radio-over-fiber system using the proposed RSH-QAM system. DSP = Digital Signal Processor.

Fig. 2.3 Description of image-band noise rejection condition of OBPF

Fig. 2.4 Calculated results for coherent (η=1/2), RSH (η=1/2 with PS = PLO), and conventional SCM systems (with m=10% and 20%).

Fig. 2.5 Measured 4-PAM eye diagram at the output of the LPF.

Fig. 2.6 Software processing of the IF data for demodulation.

Fig. 2.7 Calculated power spectral density of the sampled IF signal.

Fig. 2.8 Measured 16-QAM constellation diagram (a) back-to-back with MER = 20.58 dB (b) 100 km transmission with 2 dBm launched power with MER = 20.24 dB.

The circle points represent the ideal signal constellation, and the dashed lines are the decision thresholds.

Fig. 2.9 Spectral shape of the OBPF and the spectrum of the dual-wavelength signals in the experiment. The shorter wavelength is the modulated optical carrier, and the longer wavelength is the un-modulated optical carrier. The spectral resolution of the optical spectrum analyzer was set at 0.01 nm.

Fig. 2.10 MER dependence on optical amplifier input power: Solid circle points are the measured MER; solid and dashed lines are the calculated MER with and without the image rejection filter, respectively; dotted line is the ADC quantization noise-limited MER (with an ENOB of 5 bits).

Fig. 2.11 Measured frequency response with (solid line) and without (dotted line) equalizer, and the ideal raised cosine filter response with roll-off factor of 1(dashed line).

Fig. 2.12 Simulated result for MER dependence on SNR, considering only ISI effect due to the imperfect frequency response. Solid line represents the result without an equalizer. Dash line represents the result with the derived equalizer.

Fig. 2.13 Software processing for performance improvement through phase tracking block and ISI equalization.

Fig. 2.14 Back-to-back MER dependence on the received optical power before the preamplifier.

Fig. 2.15 Measured back-to-back signal constellation diagram with phase estimation and equalization. (a) for phase estimation block length of N = 125. (b) for phase estimation block length of N = 25.

Fig. 2.16 Simulation and experimental results for unrepeated 100 km

transmission after performance improvement through the DSP technique. The measured back-to-back MER is also shown.

Fig. 2.17 Measured signal constellation diagram after unrepeated 100 km transmission with digital compensation. (a) for launched power of –9 dBm and (b) for launched power of 10 dBm.