Channel-Aware Placement of Active and Passive Elements in Hybrid RIS-Assisted MISO Systems

Hybrid reconfigurable intelligent surfaces (HRISs) are RIS architectures with active and passive elements. In this letter, we show that the received signal-to-noise ratio (SNR) at the user can be improved with a channel-aware placement of the active elements in an HRIS whenever the channels undergo fading. We jointly design the transmit precoder, the HRIS coefficients, and the location of active and passive elements in the HRIS to maximize the SNR. We solve the underlying combinatorial non-convex optimization problem using alternating optimization and propose a low-complexity solver, which is provably near optimal. Through numerical simulations, we demonstrate that our proposed method significantly outperforms communication systems with no RIS, a fully passive RIS, and an HRIS with randomly placed active elements while often offering comparable or even better performance than systems with fully active RISs.