# Blind Phase Search with Angular Quantization Noise Mitigation for Efficient Carrier Phase Recovery
## 3 Simulation Results  
A 28-Gbaud coherent optical back-to-back transmission system is simulated in VPItransmissionMakerTM [15] to compare the performance of the proposed filtered BPS (F-BPS) scheme with that of the conventional BPS (C-BPS). A pseudorandom bit sequence is created and mapped to 16 QAM and 64 QAM to generate signals of 217 symbols of length. The generated signals are modulated on a lightwave carrier and loaded with additive white Gaussian noise (AWGN) to emulate erbium-doped fiber amplifier noise. The signals are then band pass filtered to remove out-of-band noise and directly fed into the receiver in order to isolate phase impairments from other fiber transmission impairments. A digital signal processing (DSP) based demodulator performing different DSP routines, as later shown in Section 4, is then applied.  
Figure 3 shows the OSNR sensitivity penalty versus the combined linewidth symbol duration product for 16 QAM and 64 QAM signals employing the proposed F-BPS scheme and the ordinary C-BPS scheme with a different number of test phases. For the C-BPS case, its block filter length was optimized to show the best performance for all the points in the curves in Figures 3 and 4. For the F-BPS case, in order to reduce the large amount of simulations to be carried out, the C-BPS block filter bandwidth and the proposed angular quantization noise LPF bandwidth were swept together, with the same value, in order to show the best performance for all the points in the curves in Figures 3 and 4. It can be observed that the proposed F-BPS scheme improves the phase noise tolerance of the C-BPS algorithm for both 16 QAM and 64 QAM constellations when employing the same number of test phases. The relative performance improvement of the F-BPS scheme compared to C-BPS increases for low values of \(\beta\) test phases where the quantization noise is more prominent. For 16 QAM, the C-BPS performance (@ 1 dB of OSNR penalty) employing 32 test phases can be achieved with the proposed F-BPS with only nine test phases. For 64 QAM, the corresponding numbers are 12 test phases for F-BPS compared with 64 test phases for C-BPS. As observed in Figure 3, angular quantization noise causes large performance degradation in the C-BPS when the number of employed test phases are reduced from 32 to 9 for 16 QAM and from 64 to 12 for 64 QAM. Figure 4 illustrates the tolerable linewidth symbol duration product versus the number of \(\beta\) test phases of the F-BPS and C-BPS schemes for 16 QAM and 64 QAM. The results show the achievable phase noise tolerance for 1 dB OSNR penalty at the BER FEC limits of 3.8 \(\times\) 10\({}^{-3}\) for 16 QAM and 2 \(\times\) 10\({}^{-2}\) for 64 QAM. For 16-QAM, a \(\sim\)16% phase noise tolerance increase is observed for the F-BPS compared to C-BPS, when using 32 test phases in both schemes. For 64 QAM, employing 64 test phases, a \(\sim\)31% increase of phase noise tolerance is achieved with the proposed F-BPS scheme. It is noted that the complexity of the C-BPS algorithm is directly related to the number of employed test phases and its filter block length [16]. The authors have observed that, for the same linewidth levels, similar filter block lengths were required for both the C-BPS and the F-BPS cases even when employing different numbers of test phases. Hence, for 16 QAM, a \(\sim\)72% implementation complexity reduction can be achieved with the F-BPS (\(\beta\) = 9) compared to C-BPS (\(\beta\) = 32), while maintaining the same phase noise tolerance level. The complexity reduction is even larger for 64 QAM where the reduction from \(\beta\) = 64 test phases for C-BPS to only \(\beta\)-12 test phases leads to a 81% reduction of complexity without sacrificing performance. The complexity of the sliding average filter for quantization noise mitigation is negligible compared to that of the required computations for each extra test phase.