Blind Polarization Demultiplexing of Shaped QAM Signals Assisted by Temporal Correlations

While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1], it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms are not suitable for them [2]. It is known that independently and identically distributed (iid) Gaussian signals, when mixed, cannot be recovered/separated from their mixture. For PCS-QAM signals, there are algorithms such as [3], [4] which are designed by extending conventional blind algorithms used for uniform QAM signals. In these algorithms, an initialization point is obtained by processing only a part of the mixed signal, which have non-Gaussian statistics. In this paper, we propose an alternative method wherein we add temporal correlations at the transmitter, which are subsequently exploited at the receiver in order to separate the polarizations. We will refer to the proposed method as frequency domain (FD) joint diagonalization (JD) probability aware-multi modulus algorithm (pr-MMA), and it is suited to channels with moderate polarization mode dispersion (PMD) effects. Furthermore, we extend our previously proposed JD-MMA [5] by replacing the standard MMA with a pr-MMA, improving its performance. Both FDJD-pr-MMA and JD-pr-MMA are evaluated for a diverse range of PCS (entropy $𝓗$) over a first-order PMD channel that is simulated in a proof-of-concept setup. A MMA initialized with a memoryless constant modulus algorithm (CMA) is used as a benchmark. We show that at a differential group delay (DGD) of 10% of symbol period ${\text{T}}_{\text{symb}}$ and 18 dB SNR/pol., JD-pr-MMA successfully demultiplexes the PCS signals, while CMA-MMA fails drastically. Furthermore, we demonstrate that the newly proposed FDJD-pr-MMA is robust against moderate PMD effects by evaluating it over a DGD of up to 40% of ${\text{T}}_{\text{symb}}$. Our results show that the proposed FDJD-pr-MMA successfully equalizes PMD channels with a DGD up to 20% of ${\text{T}}_{\text{symb}}$.