Double-RIS Communication with DF Relaying for Coverage Extension: Is One Relay Enough?

In this work, we investigate the decode-and-forward (DF) relay-aided double reconfigurable intelligent surface (RIS)-assisted networks, where the signal is subject to reflections from two RISs before reaching the destination. Different relay-aided network architectures are considered for maximum achievable rate under a total power constraint. Phase optimization for the double-RIS channels is tackled via the alternating optimization and majorization-minimization (MM) schemes. Moreover, closed-form solutions are obtained for each case. Numerical results indicate that the deployment of two relays, one near each RIS, achieves higher rates at low and medium signal-to-noise ratios (SNRs) compared to placing a single relay between the two RISs; while at high SNRs, the latter approach achieves higher rates only if the inter-relay interference for the former case is considerably high.