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In this work, we study the outage probability (OP) at the destination of anintelligent reflecting surface (IRS) assisted communication system in a$\kappa-\mu$ fading environment. A practical system model that takes intoaccount 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 simpleapproximations for the OP using the following approaches: (i) uni-variatedimension reduction, (ii) moment matching and, (iii) Kullback-Leiblerdivergence minimization. The resulting expressions for OP are simple toevaluate and quite tight even in the tail region. The validity of theseapproximations is demonstrated using extensive Monte Carlo simulations. We alsostudy the impact of the number of bits available for quantization, the positionof IRS with respect to the source and destination and the number of IRSelements on the OP for systems with and without an SD link.

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