Ultrafast and low overhead training symbol based channel estimation in coherent M-QAM single-carrier transmission systems

Abstract

We propose a training symbol based channel estimation (TS-EST) algorithm that estimates the 2 × 2 Jones channel matrix. The estimated matrix entries are then used as the initial center taps of the 2 × 2 butterfly equalizer. Employing very few training symbols for TS-EST, ultrafast polarization tracking is achieved and tap update can be initially pursued using the decision-directed least mean squares (DD-LMS) algorithm to mitigate residual intersymbol interference (ISI). We experimentally verify the proposed TS-EST algorithm for 112 Gbps PDM-QPSK and 224 Gbps PDM-16QAM systems using 10 and 40 training symbols for TS-EST, respectively. Steady-state and transient bit error rates (BERs) achieved using the TS-EST algorithm are compared to those obtained using the constant modulus algorithm (CMA) and the training symbol least mean squares (TS-LMS) algorithm and results show that the proposed TS-EST algorithm provides the same steady-state BER with a superior convergence speed. Also, the tolerance of the proposed TS-EST algorithm to laser phase noise and fiber nonlinearity is experimentally verified. Finally, we show by simulation that the superior tracking speed of the TS-EST algorithm allows not only for initial polarization tracking but also for tracking fast polarization transients if four training symbols are periodically sent during steady-state operation with an overhead as low as 0.57%.

Research Progress on Carrier-Free Phase-Retrieval Receivers

“…Experimental results have shown that the In order to accomplish the polarization demultiplexing in dual-polarization CF-PR receiver, the scheme of using training sequence to estimate the fiber transfer matrix is proposed in [47], as shown in Figure 12. This scheme uses 300 consecutive training symbols to obtain the fiber transfer matrix h = h CD * h PM [75][76][77][78], by multiplying the received training symbols with the pseudo inverse of time-aligned transmitted training symbols. By running the phase retrieval algorithm and channel estimation iteratively, the fiber transfer matrix h, containing both the polarization rotation and CD, can be properly recovered.…”

Experimental Investigation on Low-Complexity Adaptive Equalizer Including RSOP Tracking and Phase Recovery for 112 Gb/s PDM-QPSK Transmission System

“…But it will get a little higher complexity when the number of FIR taps is relatively few. Modern fibers have very small polarization mode dispersion (PMD) parameters (<0.1 ps/km 1/2 ) [10], and thus two kinds of similar simplified time-domain AEQs have also been reported in [11], [12]. K. Matsuda has proposed a simplified AEQ constituted with a 1-tap butterfly FIR filter for polarization de-multiplexing and two N-tap FIR filters for adaptive equalization, and PMD compensation is neglected (hereinafter referred to 1-N structure) [11].…”