Phase Calibration for Intelligent Reflecting Surfaces Assisted Millimeter Wave Communications

In this paper, wepropose a novel two-stage transmission framework for an intelligent reflecting surface (IRS) assisted millimeter wave (mmWave) system in the presence of phase error caused by hardware impairments. Specifically, in Stage I, we introduce a pilot-based phase calibration task and reformulate it as an alternating optimization program. Building on this formulation, an efficient iterative algorithm is developed to jointly estimate the phase error, which needs to be calibrated, and the channels corresponding to the first user. Stage II consists of two blocks, channel estimation and data transmission. During the channel estimation block, by leveraging on the sparsity of mmWave channels, we propose a fast Fourier transform based scheme to estimate the IRS-BS channel and user-IRS channels. During the data transmission block, based on the estimated channel state information, base station precoders and IRS phase shifts are jointly optimized to maximize the sum signal-to-leakage-plus-noise ratio of all users. To handle this non-convex problem, we further develop a low-complexity joint beamforming algorithm by exploiting fractional programming techniques. Moreover, to examine the performance of the proposed phase calibration scheme, we derive the Cramer-Rao lower bound for the intended phase error estimation. Simulation results validate the effectiveness of our proposed transmission framework and the necessity of IRS phase calibration.