Spectral Efficiency Analysis of Hybrid Relay-Reflecting Intelligent Surface-Assisted Cell-Free Massive MIMO Systems

A cell-free (CF) massive multiple-input-multiple-output (mMIMO) system can provide uniform spectral efficiency (SE) with simple signal processing. On the other hand, a recently introduced technology called hybrid relay-reflecting intelligent surface (HR-RIS) can customize the physical propagation environment by simultaneously reflecting and amplifying radio waves in preferred directions. Thus, it is natural that incorporating HR-RIS into CF mMIMO can be a symbiotic convergence of these two technologies for future wireless communications. This motivates us to consider an HR-RIS-aided CF mMIMO system to utilize their combined benefits. We first model the uplink/downlink channels and derive the minimum-mean-square-error estimate of the effective channels. We then present a comprehensive analysis of SE performance of the considered system. Specifically, we derive closed-form expressions for the uplink and downlink SE. The results reveal important observations on the performance gains achieved by HR-RISs compared to conventional systems. The presented analytical results are also valid for conventional CF mMIMO systems and those aided by passive reconfigurable intelligent surfaces. Such results play an important role in designing new transmission strategies and optimizing HR-RIS-aided CF mMIMO systems. Finally, we provide extensive numerical results to verify the analytical derivations and the effectiveness of the proposed system design under various settings.