In this study, the performance of intelligent reflecting surfaces (IRSs) with a discrete phase shift strategy is examined in multiple-antenna systems. Considering the IRS network overhead, the achievable rate model is newly designed to evaluate the practical IRS system performance. Finding the optimal resolution of the IRS discrete phase shifts and a corresponding phase shift vector is an NP-hard combinatorial problem with an extremely large search complexity. Recognizing the performance trade-off between the IRS passive beamforming gain and IRS signaling overheads, the incremental search method is proposed to present the optimal resolution of the IRS discrete phase shift. Moreover, two low-complexity sub-algorithms are suggested to obtain the IRS discrete phase shift vector during the incremental search algorithms. The proposed incremental search-based discrete phase shift method can efficiently obtain the optimal resolution of the IRS discrete phase shift that maximizes the overhead-aware achievable rate. Simulation results show that the discrete phase shift with the incremental search method outperforms the conventional analog phase shift by choosing the optimal resolution of the IRS discrete phase shift. Furthermore, the cumulative distribution function comparison shows the superiority of the proposed method over the entire coverage area. Specifically, it is shown that more than 20% of coverage extension can be accomplished by deploying IRS with the proposed method.
Keywords: block coordinate descent; discrete phase shift; greedy algorithm; incremental search; intelligent reflecting surface; signaling overhead.