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As a new technology to reconfigure wireless communication environment bysignal reflection controlled by software, intelligent reflecting surface (IRS)has attracted lots of attention in recent years. Compared with conventionalrelay system, the relay system aided by IRS can effectively save the cost andenergy consumption, and significantly enhance the system performance. However,the phase quantization error generated by IRS with discrete phase shifter maydegrade the receiving performance of the receiver. To analyze the performanceloss arising from IRS phase quantization error, in accordance with the law oflarge numbers and Rayleigh distribution, the closed-form expressions for thesignal-to-noise ratio (SNR) performance loss and achievable rate of the doubleIRS-aided amplify-and-forward (AF) relay network, which are associated with thenumber of phase shifter quantization bits, are derived in the Rayleighchannels. In addition, their approximate performance loss closed-formexpressions are also derived based on the Taylor series expansion. Simulationresults show that the performance losses of SNR and achievable rate decreasewith the number of quantization bits increases gradually, and increase with thenumber $k$ of IRS phase shift elements. The SNR and achievable rate performancelosses of the system are smaller than 0.06dB and 0.03bits/s/Hz when $k$ isequal to 4 and 3, respectively.

Performance Analysis of Discrete-Phase-Shifter IRS-aided Amplify-and-Forward Relay Network