Iterative channel estimation and data detection algorithm for MIMO-OTFS systems

Channel estimation in high-mobility environments is a challenging problem for advanced mobile communication systems (5G and beyond). In this manuscript, we first propose an iterative algorithm for channel estimation and data detection in the delay-Doppler domain for multiple-input multiple-output orthogonal time frequency space system. Then, in order to increase the spectral efficiency of the system, we use a superimposed pilot pattern. The proposed algorithm takes advantage from the sparse nature of the channel in the delay-Doppler domain and iterates between message passing-aided data detection and data-aided channel estimation. For channel estimation, we propose two algorithms. The first one consists in estimating all channel parameters, including the number of path gains, delay taps, Doppler taps, and channel gains by using a mean-field approximation and the variational Bayesian expectation maximization algorithm. The second one, based on the fact that delay and Doppler taps remain unchanged for a rather long period of time, uses an MMSE approach combined with Cholesky decomposition to only estimate channel gains in each transmitted frame. For data detection, we adapt the message-passing algorithm proposed in the literature. We also derive a lower bound on the signal-to-interference-plus-noise ratio of the proposed scheme, and maximize it by optimally allocating power between pilots and data symbols. Finally, we compare the complexity and the performance in terms of normalized mean square error, bit error rate, and spectral efficiency against existing methods. Simulation results, conducted in high-mobility scenarios show that the proposed algorithm achieves a good compromise between complexity and performance.