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In this paper, we address the problem of joint downlink (DL) and uplink (UL) channel estimation for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. Assuming a closed-loop and multifrequency-based channel training framework in which pilot signals received by multiple antenna mobile stations (MSs) are coded and spread in the frequency domain via multiple adjacent subcarriers, we propose two tensor-based semiblind receivers by capitalizing on the multilinear structure and sparse feature of the received signal at the BS equipped with a hybrid analog-digital beamforming (HB) architecture. As a first processing stage, the joint estimation of the compressed DL and UL channel matrices can be obtained in an iterative way by means of an alternating least squares (ALS) algorithm that capitalizes on a parallel factors model for the received signals. Alternatively, for more restricted scenarios, a closed-form solution is also proposed. From the estimated effective channel matrices, the users’ channel parameters such as angles of departure (AoD), angles of arrival (AoA), and path gains are then estimated in a second processing stage by solving independent compressed sensing (CS) problems (one for each MS). In contrast to the classical approach in the literature, in which the DL and UL channel estimation problems are usually considered as two separate problems, our idea is to jointly estimate both the DL and UL channels as a single problem by concentrating most of the processing burden for channel estimation at the BS side. Simulation results demonstrate that the proposed receivers achieve a performance close to the classical approach that is applied on DL and UL communication links separately, with the advantage of avoiding complex computations for channel estimation at the MS side as well as dedicated feedback channels for each MS, which are attractive features for massive MIMO systems.

Joint DL and UL Channel Estimation for Millimeter Wave MIMO Systems Using Tensor Modeling