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Most works in IRS-assisted systems have ignored the impact of the inevitableresidual hardware impairments (HWIs) at both the transceiver hardware and theIRS while any relevant works have addressed only simple scenarios, e.g., withsingle-antenna network nodes and/or without taking the randomness of phasenoise at the IRS into account. In this work, we aim at filling up this gap byconsidering a general IRS-assisted multi-user (MU) multiple-input single-output(MISO) system with imperfect CSI and correlated Rayleigh fading. In parallel,we present a general computationally efficient methodology for IRS reflectbeamforming (RB) optimization. Specifically, we introduce an advantageouschannel estimation (CE) method for such systems accounting for the HWIs.Moreover, we derive the uplink achievable spectral efficiency (SE) withmaximal-ratio combining (MRC) receiver, displaying three significant advantagesbeing: 1) its closed-form expression, 2) its dependence only on large-scalestatistics, and 3) its low training overhead. Notably, by exploiting the firsttwo benefits, we achieve to perform optimization with respect to the reflectbeamforming matrix (RBM) that can take place only at every several coherenceintervals, and thus, reduces significantly the computational cost compared toother methods which require frequent phase optimization. Among the insightfulobservations, we highlight that uncorrelated Rayleigh fading does not allowoptimization of the SE, which makes the application of an IRS ineffective.Also, in the case that the phase drifts, describing the distortion of thephases in the RBM, are uniformly distributed, the presence of an IRS providesno advantage. The analytical results outperform previous works and are verifiedby Monte-Carlo (MC) simulations.

Intelligent Reflecting Surface-assisted MU-MISO Systems with Imperfect Hardware: Channel Estimation, Beamforming Design