Abstract
Using coherent optical detection and digital signal processing, laser phase noise and equalization enhanced phase noise can be effectively mitigated using the feed-forward and feed-back carrier phase recovery approaches. In this paper, theoretical analyses of feed-back and feed-forward carrier phase recovery methods have been carried out in the long-haul high-speed n-level phase shift keying (n-PSK) optical fiber communication systems, involving a one-tap normalized least-mean-square (LMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm. The analytical expressions for evaluating the estimated carrier phase and for predicting the bit-error-rate (BER) performance (such as the BER floors) have been presented and discussed in the n-PSK coherent optical transmission systems by considering both the laser phase noise and the equalization enhanced phase noise. The results indicate that the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms for small phase noise variance (or effective phase noise variance), while the one-tap normalized LMS algorithm shows a better performance than the other two algorithms for large phase noise variance (or effective phase noise variance). In addition, the one-tap normalized LMS algorithm is more sensitive to the level of modulation formats.
Highlights
Since the first generation of optical fiber communication systems was deployed over 30 years ago, the achievable data rates carried by a single optical fiber have been raised over 10,000 times, and the data network traffic has been increased by over a factor of 100 [1,2]
To compensate the phase noise from the laser sources, some feed-forward and feed-back carrier phase recovery (CPR) approaches have been proposed to estimate and remove the phase of optical carriers [23,24,25,26,27,28,29,30,31,32]. Among these carrier phase estimation (CPE) methods, the one-tap normalized least-mean-square (LMS) algorithm, the block-wise average (BWA) algorithm, and the Viterbi-Viterbi (VV) algorithm have been validated for mitigating the laser phase noise effectively, and are regarded as the most promising digital signal processing (DSP) algorithms in the real-time implementation of the high-speed coherent optical fiber transmission systems [27,28,29,30,31,32]
The complexity of the one-tap normalized LMS, the block-wise average, and the Viterbi-Viterbi carrier phase recovery algorithms has been investigated in terms of the number of the complex multiplications per recovered symbol, which are shown in Table 1 (n is the level of modulation formats)
Summary
Since the first generation of optical fiber communication systems was deployed over 30 years ago, the achievable data rates carried by a single optical fiber have been raised over 10,000 times, and the data network traffic has been increased by over a factor of 100 [1,2]. Built on the previous work in [26,37,51], the theoretical assessments of the carrier phase recovery using the one-tap normalized LMS, the block-wise average, and the Viterbi-Viterbi algorithms are extended and analyzed in detail for the long-haul high speed n-PSK coherent optical fiber communication systems, considering both the intrinsic laser phase noise and the equalization enhanced phase noise. Found that the one-tap normalized LMS algorithm is more sensitive to the level of the modulation formats than the other two algorithms
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