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

Intelligent reflecting surface (IRS), consisting of lowcost
passive elements, is a promising technology for improving
the spectral and energy efficiency of the fifth-generation (5G)
and beyond networks. It is also noteworthy that an IRS can
shape the reflected signal propagation. Most works in IRSassisted
systems have ignored the impact of the inevitable residual
hardware impairments (HWIs) at both the transceiver hardware
and the IRS while any relevant works have addressed only simple
scenarios, e.g., with single-antenna network nodes and/or without
taking the randomness of phase noise at the IRS into account.
In this work, we aim at filling up this gap by considering a
general IRS-assisted multi-user (MU) multiple-input single-output
(MISO) system with imperfect channel state information (CSI)
and correlated Rayleigh fading. In parallel, we present a general
computationally efficient methodology for IRS reflect beamforming
(RB) optimization. Specifically, we introduce an advantageous
channel estimation (CE) method for such systems accounting for
the HWIs. Moreover, we derive the uplink achievable spectral
efficiency (SE) with maximal-ratio combining (MRC) receiver,
displaying three significant advantages being: 1) its closed-form
expression, 2) its dependence only on large-scale statistics, and
3) its low training overhead. Notably, by exploiting the first two
benefits, we achieve to perform optimization with respect to the
that can take place only at every several coherence intervals,
and thus, reduces significantly the computational cost compared
to other methods which require frequent phase optimization.
Among the insightful observations, we highlight that uncorrelated
Rayleigh fading does not allow optimization of the SE, which
makes the application of an IRS ineffective. Also, in the case that
the phase drifts, describing the distortion of the phases in the
RBM, are uniformly distributed, the presence of an IRS provides
no advantage. The analytical results outperform previous works
and are verified by Monte-Carlo (MC) simulations.