Diversity and SEP Analysis of IRS-Assisted Systems in Correlated Rayleigh Fading Channels

Intelligent reflecting surfaces (IRSs) are a promising technology to enhance communication system performance as they can reflect signals in a manner that the reflected signals combine coherently at the receiver. Since many IRS elements are often closely spaced on the surface, the channel gains between IRS elements are correlated. An exact analysis of diversity order and symbol error probability (SEP) is infeasible as the distribution of the instantaneous signal-to-noise ratio (SNR) has no tractable, closed-form expression. We use SNR bounds to circumvent this issue and show that for an IRS-assisted system with no direct link between the transmitting access point (AP) and receiving user, the diversity order is upper bounded by the minimum rank among the AP-IRS and IRS-user correlation matrices and lower bounded by the maximum number of IRS elements with full-rank correlation matrices for the AP-IRS and IRS-user links. Using the SNR bounds, we also derive SEP bounds. While the SEP lower bound is seen to be tight, the SEP upper bound is tight only when the number of IRS elements is small.