Sparse Bayesian Learning Based Tensor Dictionary Learning and Signal Recovery With Application to MIMO Channel Estimation

摘要

In this paper, we develop solutions for sparse tensor signal recovery (SR) and tensor dictionary learning (DL) problems via the sparse Bayesian learning (SBL) approach. We consider a class of tensor system which has the special sparsity structure that a given (say the ith) row of every unfolding matrices of the tensor involved is simultaneously zero or non-zero. For both problems, we propose a Kronecker-like prior distribution for the variables to be recovered in the framework of SBL to take advantage of this sparsity structure. For tensor DL, we consider a de-noising problem in which the clear version is recoverable from sparse coefficients and several separable dictionaries. Our prior distribution model for sparse coefficients entails that the same column of these separable dictionaries have a common prior distribution. We show that our SBL-based algorithms for solving the SR and DL problems require much lower complexity than that of the corresponding vector-matrix system by reducing the matrix inversion size. The proposed SBL-DL and SBL-SR algorithms are utilized, invoking a tensor virtual channel model, to estimate the channel response of a millimeter wave communication system which employs uniform planar arrays on both sides. The superiority of the resulting channel estimates is verified by computer simulations.