Tensor Rank Regularization with Bias Compensation for Millimeter Wave Channel Estimation

Abstract

This paper presents a novel method of tensor rank regularization with bias compensation for channel estimation in a hybrid millimeter wave MIMO-OFDM system. Channel estimation is challenging due to the unknown number of multipath components that determines the channel rank. In general, finding the intrinsic rank of a tensor is a non-deterministic polynomial-time (NP) hard problem. However, by leveraging the sparse characteristics of millimeter wave channels, we propose a modified CANDECOMP/PARAFAC (CP) decomposition-based method that jointly estimates the tensor rank and channel component matrices. Our approach differs from most existing works that assume the number of channel paths is known and the proposed method is able to estimate channel parameters accurately without the prior knowledge of number of multipaths. The objective of this work is to estimate the tensor rank by a novel sparsity-promoting prior that is incorporated into a standard alternating least squares (ALS) function. We introduce a weighting parameter to control the impact of the previous estimate and the tensor rank estimation bias compensation in the regularized ALS. The channel information is then extracted from the estimated component matrices. Simulation results show that the proposed scheme outperforms the baseline l1 strategy in terms of accuracy and robustness. It also shows that this method significantly improves rank estimation success at the expense of slightly more iterations.