Low Complexity Carrier Recovery Based on Gradient Descent for Optical Communication

A carrier recovery algorithm based on gradient descent with parallelized architecture is proposed for BPSK/QPSK modulated optical communication, and the recovery performance has been validated experimentally. A simplified Mth-power operation implementation method is introduced, which considerably lowers the algorithm complexity. Experimental results demonstrate that, with the proposed algorithm in this letter, both quick tracking ability and stable estimation accuracy comparable to the LKF-based algorithm can be achieved, which is better than the traditional FFT&VV and Diff&VV algorithms under different SNR; moreover, for BPSK/QPSK switchable system, it can save 36.3% of CLB LUTs and 30.9% of CLB registers FPGA chip resource compared to the LKF-based algorithm, within a 64-channel FPGA-based parallel architecture.

I. Introduction

Carrier recovery (CR) in coherent optical communication is meant to compensate for the random phase noise (PN) caused by finite linewidth lasers and the frequency offset (FO) between the signal carrier and local oscillator. Many carrier recovery techniques have been proposed to implement the compensation of the FO and the PN separately or jointly [1]. The separate approach involves performing FO compensation first, followed by PN compensation. In this method, fast Fourier transform (FFT) spectrum peak search [2] or phase differential (Diff) detection [3] algorithms are commonly used for coarse FO estimation. Subsequently, then Viterbi-Viterbi (VV) [4] or blind phase search (BPS) [5] variants algorithms are employed to estimate the carrier phase. However, this approach cannot achieve high precision and real-time carrier phase estimation simultaneously [6]. Kalman filter based algorithms with decision feedback are proposed to jointly compensate the FO and PN in order to address this issue. A parallelized architecture utilizing a linear Kalman filter (LKF) was presented to enhance computational speeds [7]. Additionally, improved Kalman filtering systems based on the unscented Kalman filter (UKF) [8] and the extended Kalman filter (EKF) [9] were further proposed for CR, achieving precise state estimation at the cost of increased computational complexity. In our previous work, we proposed an adaptive square root unscented Kalman filter for CR to address the effects of atmospheric turbulence in satellite-to-earth laser communications [10]. By introducing a new observation model and updating process/measurement noise covariance adaptively, it can relax the required transmit power by up to 0.5-3 dB compared with LKF. However, all the algorithms discussed above still have the problem on high-complexity or poor real-time or performance degradation at low signal-to-noise ratio (SNR). In particular, the enhanced Kalman filtering algorithms face significant challenges in practical applications due to their increased computational complexity. These issues are unacceptable in certain specialized scenarios, such as satellite or airborne laser communication links with resource constraints and weak received power.