STAR-RIS-Aided Cell-Free Massive MIMO with Imperfect Hardware

This paper considers a simultaneously transmitting and reflecting reconfigurable intelligent surface (STARRIS)-aided cell-free massive multiple-input multiple-output (CF-mMIMO) system, accounting for imperfect hardware in spatially correlated fading channels. Specifically, we consider the hardware impairments and phase noise at transceivers, as well as the phase shift errors generated within the STAR-RIS. We commence by introducing the STAR-RIS signal model, channel model, and imperfect hardware components. Then, the linear minimum mean-square error (MMSE) channel estimate is derived with pilot contamination, which provides sufficient information for sequential data processing. Moreover, a channel capacity lower bound is derived in the case of a finite number of RIS elements and access points (APs), while a closed-form expression for the downlink ergodic spectral efficiency (SE) for maximum ratio (MR) precoding is also deduced, where only the channel statistics are used. Our numerical results demonstrate that the STAR-RIS-aided CF-mMIMO system achieves higher SE compared to the conventional CF-mMIMO system, even with imperfect hardware.