Spectral Efficiency Analysis of HybridRelay-Reflecting Intelligent Surface-AssistedCell-Free Massive MIMO Systems

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