Intelligent Reflecting Surface Aided Activity Detection for Massive Access: Performance Analysis and Learning Approach

This paper investigates a covariance-based approach for intelligent reflecting surface (IRS) aided activity detection in massive machine-type communications (mMTC). In the conventional scenario without IRS, the covariance-based approach, which exploits the probability density function (PDF) of the received signals at the base station (BS), has been demonstrated to outperform the compressed sensing approach. However, when taking the impact of the IRS into account, due to the newly introduced cascaded channels, it is difficult to obtain the exact PDF of the received signals at the BS. To tackle this challenge, we propose an approximation for the intended PDF with tunable parameters in the covariance matrix of the received signals. Based on the proposed tractable reformulation, an analytic framework is established to reveal the guideline for the phase shift design. Moreover, to determine the optimal correlation parameters, a deep unfolding approach is further leveraged by regarding them as trainable parameters. Simulation results validate the theoretical analysis and demonstrate the superior performance of the proposed learning approach.