Outage Probability Expressions for an IRS-Assisted System with and without Source-Destination Link for the Case of Quantized Phase Shifts in $kappa-mu$ fading

In this work, we study the outage probability (OP) at the destination of an intelligent reflecting surface (IRS) assisted communication system in a $kappa-mu$ fading environment. A practical system model that takes into account the presence of phase error due to quantization at the IRS when a) source-destination (SD) link is present and b) SD link is absent is considered. First, an exact expression is derived, and then we derive three simple approximations for the OP using the following approaches: (i) uni-variate dimension reduction, (ii) moment matching and, (iii) Kullback-Leibler divergence minimization. The resulting expressions for OP are simple to evaluate and quite tight even in the tail region. The validity of these approximations is demonstrated using extensive Monte Carlo simulations. We also study the impact of the number of bits available for quantization, the position of IRS with respect to the source and destination and the number of IRS elements on the OP for systems with and without an SD link.