Hybrid mmWave MIMO Systems Under Hardware Impairments and Beam Squint: Channel Model and Dictionary Learning-Aided Configuration

Low overhead channel estimation based on compressive sensing (CS) has been widely investigated for hybrid wideband millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. The channel sparsifying dictionaries used in prior work are built from ideal array response vectors evaluated on discrete angles of arrival/departure. In addition, these dictionaries are assumed to be the same for all subcarriers, without considering the impacts of hardware impairments and beam squint. In this manuscript, we derive a general channel and signal model that explicitly incorporates the impacts of hardware impairments, practical pulse shaping functions, and beam squint, overcoming the limitations of mmWave MIMO channel and signal models commonly used in previous work. Then, we propose a dictionary learning (DL) algorithm to obtain the sparsifying dictionaries embedding hardware impairments, by considering the effect of beam squint without introducing it into the learning process. We also design a novel CS channel estimation algorithm under beam squint and hardware impairments, where the channel structures at different subcarriers are exploited to enable channel parameter estimation with low complexity and high accuracy. Numerical results demonstrate the effectiveness of the proposed DL and channel estimation strategy when applied to realistic mmWave channels.

I. Introduction

The acquisition of channel state information (CSI) is crucial for mmWave link configuration, and challenging when operating with hybrid beamforming architectures. To reduce the training overhead associated with CSI acquisition, prior work has made full use of the sparse nature of mmWave channels in the angular or delay domains [1], [2], [3], [4], [5]. Nevertheless, some relevant practical aspects have not been fully considered in previous compressive channel models and estimation algorithms: the beam squint effect, calibration errors, and hardware impairments. Specifically, the channel sparsifying dictionaries used in prior work are typically assumed to be (overcomplete) discrete Fourier transform (DFT) matrices, or constructed from the ideal array response matrices (IARM) evaluated on discrete grids of quantized angles of arrivals and departures (AoAs/AoDs) [2], [4]. These assumptions are valid, however, only when the beam squint effect is negligible and no hardware impairments or calibration errors exist. In this paper, we show that under hardware impairments such as mutual coupling or antenna separation disturbances, the array response vectors will no longer be the Vandermonde vectors, and that different array response vectors should be considered at every frequency for channel modeling under beam squint. In other words, the assumptions and modeling of wideband mmWave MIMO channels in prior work are not valid, and therefore, the prior CSI acquisition strategies are not effective when beam squint and hardware impairments are considered.