hv
photonics
Article
Blind Phase Search with Angular Quantization Noise Mitigation for Efficient Carrier Phase Recovery Jaime Rodrigo Navarro 1,2, *, Aditya Kakkar 1,2 , Richard Schatz 2 , Xiaodan Pang 2 , Oskars Ozolins 1 , Aleksejs Udalcovs 1 , Sergei Popov 2 and Gunnar Jacobsen 1 1 2
*
Networking and Transmission Laboratory, RISE Acreo AB, SE-164 40 Kista, Sweden;
[email protected] (A.K.);
[email protected] (O.O.);
[email protected] (A.U.);
[email protected] (G.J.) School of Engineering Sciences, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden;
[email protected] (R.S.);
[email protected] (X.P.);
[email protected] (S.P.) Correspondence:
[email protected]; Tel.: +46-76-282-77-40
Received: 19 April 2017; Accepted: 18 May 2017; Published: 23 May 2017
Abstract: The inherent discrete phase search nature of the conventional blind phase search (C-BPS) algorithm is found to introduce angular quantization noise in its phase noise estimator. The angular quantization noise found in the C-BPS is shown to limit its achievable performance and its potential low complexity implementation. A novel filtered BPS algorithm (F-BPS) is proposed and demonstrated to mitigate this quantization noise by performing a low pass filter operation on the C-BPS phase noise estimator. The improved performance of the proposed F-BPS algorithm makes it possible to significantly reduce the number of necessary test phases to achieve the C-BPS performance, thereby allowing for a drastic reduction of its practical implementation complexity. The proposed F-BPS scheme performance is evaluated on a 28-Gbaud 16QAM and 64QAM both in simulations and experimentally. Results confirm a substantial improvement of the performance along with a significant reduction of its potential implementation complexity compared to that of the C-BPS. Keywords: blind phase search (BPS); carrier phase estimation (CPE); carrier phase recovery (CPR); coherent detection; quadrature amplitude modulation (mQAM); phase noise
1. Introduction Carrier phase recovery (CPR) is an essential block to estimate and compensate for the phase noise introduced by the free running lasers in coherent optical communication systems. Two approaches for CPR are conventionally employed based on either the M-th power operation [1] or on the conventional blind phase search (C-BPS) algorithm [2]. The M-th power operation approach provides a poorer phase noise tolerance for high order constellations as only a small percentage of constellation points can be employed for phase noise estimation. Additionally, the accuracy of symbol amplitude discrimination required for symbol classification or partitioning in this approach decreases for low optical to signal noise ratios (OSNRs) or high order constellations [3–5]. On the other hand, the C-BPS approach provides high phase noise tolerance at the expense of a high computational complexity. The number of required test phases to achieve high phase noise tolerance largely increases with the modulation order which increases the overall computational complexity of the algorithm and becomes a burden for its practical implementation. Alternatively, multi-stage CPR schemes employing both approaches in different stages have also been proposed with the aim of providing good phase noise tolerance while maintaining a relatively low overall computational complexity [3–12]. However, the implementation complexity reductions achieved by the proposed multi-stage algorithms are not the minimum achievable and could be further reduced by overcoming the inherent limitations of the C-BPS stage provided in this manuscript. High phase noise tolerant CPR schemes at low implementation complexity levels would make it possible to use smaller integrated DFB lasers, driven Photonics 2017, 4, 37; doi:10.3390/photonics4020037
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smaller integrated DFB lasers, driven at low power for high order modulations or DBR lasers with electronic tuning via carrier injection instead of thermal tuning. at low for high order modulations or DBRlimitation lasers with via carrier In power this paper, we demonstrate the inherent of electronic the C-BPStuning algorithm due to injection angular instead of thermal tuning. quantization noise and propose a cost effective solution to mitigate it, using a post-BPS low pass this The paper, we demonstrate the(F-BPS) inherent limitation of thethe C-BPS algorithm due to while angular filter In (LPF). proposed filtered BPS scheme increases phase noise tolerance it quantization noise and propose a cost effective solution to mitigate it, using a post-BPS low pass reduces the computational complexity compared to that of the C-BPS. The performance of the F-BPS filter (LPF). proposed filtered and BPS 64QAM (F-BPS) through scheme increases theExperimental phase noise tolerance algorithm is The evaluated for 16QAM simulations. validationwhile of theit reduces the computational complexity compared to that of the C-BPS. performance of the F-BPS F-BPS scheme on a 28-Gbaud 64QAM is also performed. Results showThe a noticeable enhancement in algorithm is evaluated for 16QAM and 64QAM through simulations. Experimental validation of the the phase noise tolerance of the proposed F-BPS scheme compared to C-BPS and an achievable F-BPS scheme onof a 28-Gbaud 64QAMcomplexity is also performed. Results implementation. show a noticeable enhancement in drastic reduction its computational for its practical the phase noise tolerance of the proposed F-BPS scheme compared to C-BPS and an achievable drastic reduction ofof itsthe computational complexity for its practical 2. Principle Proposed Angular Quantization Noiseimplementation. Filter in F-BPS
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The operation principle Angular of the proposed F-BPSNoise scheme is in illustrated 2. Principle of the Proposed Quantization Filter F-BPS in Figure 1. As in the C-BPS, a block of 2M + 1 symbols is rotated by a number of test phases B. The resulting rotated The operation principle of the proposed F-BPS scheme is illustrated in Figure 1. As in the C-BPS, blocks of symbols for each of the test phases are then fed into a decision circuit module where the a block of 2M + 1 symbols is rotated by a number of test phases B. The resulting rotated blocks of closest constellation points in the original constellation are determined. The squared distances of 2M symbols for each of the test phases are then fed into a decision circuit module where the closest + 1 symbols to its closest constellation points in the original constellation are calculated for each of constellation points in the original constellation are determined. The squared distances of 2M + 1 the rotated block of symbols. The sum of 2M + 1 square distances is considered for averaging the symbols to its closest constellation points in the original constellation are calculated for each of the impact of additive white Gaussian noise (AWGN), which is known as the C-BPS block filter [2]. The rotated block of symbols. The sum of 2M + 1 square distances is considered for averaging the impact angular rotation providing the minimum distance metric sum is considered to be the phase noise of additive white Gaussian noise (AWGN), which is known as the C-BPS block filter [2]. The angular estimator for the symbol in the middle of the block. An unwrap module is then required to minimize rotation providing the minimum distance metric sum is considered to be the phase noise estimator cycle slip occurrence. The phase noise estimator after the unwrap module corresponds to the final for the symbol in the middle of the block. An unwrap module is then required to minimize cycle slip estimator in the C-BPS algorithm ( ˆ ). It is worth noting that ˆ has been selected from a set of occurrence. The phase noise estimator after the unwrap module corresponds to the final estimator in discrete angular values. quantization noise it is angular employed for ˆ contains ˆ ItTherefore, the C-BPS algorithm ( β). is worth noting that βˆ has been selected fromand, a setwhen of discrete values. phase noiseβˆ contains compensation as in the C-BPS, angular quantization noise in the corrected Therefore, quantization noise and, results when itin is employed for phase noise compensation as in signal. the C-BPS, results in angular quantization noise in the corrected signal.
Delay Conventional Blind Phase Search
Proposed F-BPS
Figure 1. Block Block diagram diagram of of the the C-BPS C-BPS CPR CPR scheme scheme and and the the proposed proposed F-BPS F-BPS scheme scheme employing employing the the Figure angular quantization quantization noise noise filter. filter. angular
Figure Figure 2a 2a shows shows the the frequency frequency noise noise spectrum spectrum (FN-PSD) (FN-PSD) of of the the phase phase tracked tracked by by the the C-BPS C-BPS ˆ ˆ ) for algorithm for different different values values of of test test phases phases in in aa sliding sliding window window CPR CPR approach. approach. Increased algorithm (( β) Increased frequency C-BPS phase phaseestimator estimatorisisobserved observedwith withdecreased decreasednumber numberofoftest test phases. This frequency noise in the C-BPS phases. This is is due thediscrete discretephase phasesearch searchnature natureofofthe theC-BPS C-BPSalgorithm, algorithm, introducing introducing quantization noise in due totothe in its its phase phase noise noise estimator. estimator. The The first first observed observed dip dip in in Figure Figure 2a (see ββ == 64 64 curve) curve) corresponds corresponds to to the the C-BPS C-BPS block block filter filter bandwidth bandwidth which which defines defines the the estimation estimation bandwidth bandwidth of of the the C-BPS. C-BPS. It It is is observed observed how how the the out-of-band out-of-band frequency frequency components components increase increase as as the the number number of of employed employed test test phases phases reduces reduces due due to to angular angular quantization quantization noise. noise. Figure Figure 2b 2b shows shows the the temporal temporal quantized quantized phase phase evolution evolution tracked tracked ˆ ˆ by the numbers of testofphases and a sliding approach. by the C-BPS C-BPSalgorithm algorithm( β)( for) different for different numbers test phases and awindow sliding CPR window CPR The discrete angular jumps due to angular quantization in the C-BPS are bigger for lower values of approach. The discrete angular jumps due to angular quantization in the C-BPS are bigger for lower employed phases which translates intotranslates larger quantization noise as illustrated correspondingly in values of test employed test phases which into larger quantization noise as illustrated correspondingly in Figure 2a. The proposed F-BPS scheme shown in Figure 1 uses an angular
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Figure 2a. The proposed F-BPS scheme shown Figure 1 usesperformed an angularon quantization noisenoise filter quantization noise filter consisting of a low pass in filter operation the C-BPS phase consistingtoofmitigate a low pass filter operation performed on thenoise. C-BPS phase noise angular estimator to mitigate estimator its out-of-band angular quantization The proposed quantization its out-of-band quantization noise. Thethat proposed angular quantization noise filter in the noise filter in theangular F-BPS must be designed such it removes the out-of-band noise enhancement F-BPSpreserving must be designed suchinformation that it removes out-of-band while preserving while the in band of thethe original C-BPS noise phaseenhancement estimator contained within the the in band information of the original C-BPS phase estimator contained within the C-BPS C-BPS block filter bandwidth (see Figure 2a). The improved F-BPS phase noise estimator ( ˆ f ) block after filter bandwidth (see Figure 2a). The improved F-BPS phase noise estimator ( βˆ f ) after the proposed the proposed angular quantization noise filter is then used to compensate for the phase noise of the angular quantization noise filter is then used to compensate for the phase noise of the original signal original signal as illustrated in Figure 1. as illustrated in Figure 1.
C-BPS Estimation Bandwidth (M=8)
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Figure 2. 2. (a) (a) FN-PSD FN-PSD of of different different tracked number of Figure tracked phases phasesby bythe theC-BPS C-BPSalgorithm algorithmemploying employingdifferent different number test phases; (b) time domain tracked phase by the C-BPS algorithm for different number of test phases. of test phases; (b) time domain tracked phase by the C-BPS algorithm for different number of test phases.
In practice, the need of the proposed filter is justified as the angular resolution of the C-BPS Inestimator practice, (β) the isneed of the proposed filterthe is justified as of the of the used C-BPS phase significantly smaller than resolution theangular digital resolution signal processor to phase estimator (β) is significantly smaller than the resolution of the digital signal processor used to perform the algorithm. As an example, 32 and 64 possible test phase values or less (equivalent to
