Bp-Vb-Ep Based Static And Dynamic Sparse Bayesian Learning With Kronecker Structured Dictionaries

In many applications such as massive multi-input multi-output (MIMO) radar, massive MIMO channel estimation, speech processing, image and video processing, the received signals are tensors. In such applications, utilizing techniques from tensor algebra can be beneficial since it retains the tensorial structure in the received signal compared to processing on the matricized version of the same signal. Furthermore, the underlying parameters or states to be estimated are sparse in many of the above-said applications compared to the large system dimensions. In this paper, we propose techniques which allow handling the extension of sparse Bayesian learning (SBL) to time-varying states. Adding the parameters of the autoregressive process which is used to the model the time-varyings of the state leads to a non-linear (at least bilinear) state-space model. Belief propagation (BP) is a promising method to compute the minimum mean squared error (MMSE) or maximum a posteriori (MAP) estimates, but at the the expense of a high computational burden. However, inspired by a previous work on a combined BP and variational Bayes (VB) technique, we noted that using a combination of BP, VB, and expectation propagation (EP) can help to alleviate the computational complexity.