Outage Probability and Finite-SNR DMT Analysis for IRS-Aided MIMO Systems: How Large IRSs Need to be?

Intelligent reflecting surfaces (IRSs) are promising enablers for high-capacity wireless communication systems by constructing favorable channels between the transmitter and receiver. However, general, accurate, and tractable outage probability analysis for IRS-aided multiple-input-multiple-output (MIMO) systems is not available in the literature. In this paper, we first characterize the distribution of the mutual information (MI) for IRS-aided MIMO systems by capitalizing on large random matrix theory (RMT). Based on this result, a closed-form approximation for the outage probability is derived and a gradient-based algorithm is proposed to minimize the outage probability with statistical channel state information (CSI). We also investigate the diversity-multiplexing tradeoff (DMT) with finite signal-to-noise ratio (SNR). Based on these theoretical results, we further study the impact of the IRS size on system performance. In the high SNR regime, we provide closed-form expressions for the ergodic mutual information (EMI) and outage probability as a function of the IRS size, which analytically reveal that the benefit of increasing the IRS size saturates quickly. Simulation results validate the accuracy of the theoretical analysis and confirm the increasing cost to improve system performance by deploying larger IRSs. For example, for an IRS-aided MIMO system with 20 antennas at both the transmitter and receiver, we need to double the size of the IRS to increase the throughput from 90% to 95% of its maximum value.