Low-complexity Carrier Phase Recovery Research Articles

Low-Overhead Low-Complexity Carrier Phase Recovery Technique for Coherent Multi-Band OFDM-Based Superchannel Systems Enabled by Optical Frequency Combs

Abstract In this paper, we have designed a low-overhead low-complexity carrier phase tracking scheme for OFDM-based superchannel transmission system enabled by optical frequency combs. In this scheme, taking advantage of the broadband phase coherence provided by optical frequency combs among the OFDM-bands, the carrier phase retrieved from pilot-subcarriers of the OFDM-band on the central wavelength channel is reused for the OFDM-bands on the other wavelength channels. In this case, the overall pilot-subcarrier overhead and DSP complexity is significantly reduced since the pilot-subcarriers occupy a small fraction of the overall OFDM bandwidth. The feasibility of this joint-carrier phase tracking scheme has been verified successfully via comprehensive simulation, where results show that the BER threshold for soft-decision FEC could be achieved for 50GHz-spaced 5-band 4-QAM, 8-QAM, 16-QAM and 32-QAM OFDM-based superchannel signals with zero guard-band and both laser and nonlinear phase noise effects after 7000km, 4000km, 3000km and 2000km SSMF transmission respectively. The simulation results show that there exist chromatic dispersion-induced differential phase offset among the OFDM-bands whose impact on joint-carrier phase tracking depends on the modulation format, channel count and fiber length. Finally, we demonstrate experimentally the feasibility performance of the designed master-slave carrier phase tracking technique for comb-based OFDM-based superchannels.

Low-complexity carrier phase recovery based on principal component analysis for square-QAM modulation formats.

We propose, numerically analyze and experimentally demonstrate a low-complexity, modulation-order independent, non-data-aided (NDA), feed-forward carrier phase recovery (CPR) algorithm. The proposed algorithm enables synchronous decoding of arbitrary square-quadrature amplitude modulation (QAM) constellations and it is suitable for a realistic hardware implementation based on block-wise parallel processing. The proposed method is based on principal component analysis (PCA) and it outperforms the well-known and widely used blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) values, showing much lower cycle slip rate (CSR) both numerically and experimentally. For operation at higher SNR values, a hybrid two-stage implementation combining the proposed method and BPS is also proposed and their performance are investigated benchmarking them against the two-stage BPS (2S-BPS). The complexity of the proposed simple and hybrid methods are evaluated against 2S-BPS and computational complexity savings of 92% and 40% are expected for the simple and hybrid methods, respectively.

Vertical blind phase search for low-complexity carrier phase recovery of offset-QAM Nyquist WDM transmission

Low complexity carrier phase recovery (CPR) scheme based on vertical blind phase search (V-BPS) for M-ary offset quadrature amplitude modulation (OQAM) is proposed and numerically verified. After investigating the constellations of both even and odd samples with respect to the phase noise, we identify that the CPR can be realized by measuring the verticality of constellation with respect to different test phase angles. Then measurement without multiplication in the complex plane is found with low complexity. Furthermore, a two-stage configuration is put forward to further reduce the computational complexity (CC). Compared with our recently proposed modified blind phase search (M-BPS) algorithm, the proposed algorithm shows comparable tolerance of phase noise, but reduces the CC by a factor of 3.81 (or 3.05) in the form of multipliers (or adders), taking the CPR of 16-OQAM into account.

Low-Complexity Carrier Phase Recovery Based on Constellation Classification for M-ary Offset-QAM Signal

Low-complexity carrier phase recovery (CPR) for M-ary offset quadrature amplitude modulation (OQAM) formats is proposed and numerically verified, based on the technique of constellation classification. Although the OQAM signal has very poor tolerance to the laser linewidth due to the phase noise-induced crosstalk, we find that both even and odd samples of OQAM signal only have conventional constellation rotation with respect to phase noise. Through linear fitting of the classified constellation, carrier phase estimation can be derived from the slope of linear fitting function. Compared with our recently proposed modified blind phase search scheme, the computational complexity (CC) of proposed CPR does not increase much with the OQAM modulation level of M. Taking the CPR of 16-OQAM into account, we show that the CC can be significantly reduced by a factor of 8.47 (or 7.34) in the form of multipliers (or adders) with performance comparable to MBPS (B = 24) under the condition of Δf × T S = 5 × 10 -6 . In particular, a tolerance of linewidth and symbol duration product of 8 x 10-5, under the condition of CD = 300 ps/nm and DGD = 10 ps, can be secured for 16-OQAM, given 0.7-dB required-OSNR penalty.

Low-Complexity Carrier Phase Recovery for Square M-QAM Based on S-BPS Algorithm

Minimum distance blind phase search (BPS) algorithm has good tolerance to laser linewidth but with high computational complexity. In this letter, a novel substitution algorithm, i.e., symmetry BPS (S-BPS) is proposed for arbitrary square M-ary quadrature amplitude modulation (M-QAM) coherent optical systems. Based on the symmetry of square M-QAM, it can reduce the complexity directly by simplifying the phase error detection in the real plane and without multiplication. Taking square 4-QAM, 16-QAM, and 64-QAM as examples, the effectiveness of the proposed S-BPS algorithm is demonstrated by numerical simulations.

Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD)

The MSDD carrier phase estimation technique is derived here for optically coherent QPSK transmission, introducing the principle of operation while providing intuitive insight in terms of a multi-symbol extension of naïve delay-detection. We derive here for the first time Wiener-optimized and LMS-adapted versions of MSDD, introduce simplified hardware realizations, and evaluate complexity and numerical performance tradeoffs of this highly robust and low-complexity carrier phase recovery method. A multiplier-free carrier phase recovery version of the MSDD provides nearly optimal performance for linewidths up to ~0.5 MHz, whereas for wider linewidths, the Wiener or LMS versions provide optimal performance at about 9 taps, using 1 or 2 complex multipliers per tap.