Algorithms for joint phase estimation and decoding for MIMO systems in the presence of phase noise and quasi-static fading channels

In this paper, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators, and quasi-static fading channels. As in single-antenna systems, the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice. In this purview, we propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. Our first algorithm is obtained by means of the sum-product algorithm, where we use the multivariate Tikhonov canonical distribution approach. In our next algorithm, we derive an approximate MAP symbol detector based on the smoother-detector framework, wherein the detector is properly designed by incorporating the phase noise statistics from the smoother. The third algorithm is derived based on the variational Bayesian framework. By simulations, we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions and observe that the proposed techniques significantly outperform the other important algorithms from prior works, which are considered herein.