Optimal Multi-level ASKs for RIS-Aided Noncoherent Wireless Systems in the Presence of Direct Channel

This paper examines the effectiveness of one-sided and two-sided amplitude shift keying (ASK) modulation in a reconfigurable intelligent surface (RIS)-assisted single-input single-output wireless communication system with the presence of a direct channel between the transceiver pair. The phase shifts of the RIS elements are adjusted considering the phases of all the involved channels. The receiver employs a noncoherent maximum likelihood rule to detect the transmitted ASK signals. Novel expressions for an upper bound on symbol error probability (SEP) using the union bound technique are obtained, and an optimization problem to reduce the SEP under average transmit energy constraints is formulated and solved. Numerical results demonstrate the superior performance of the optimized ASKs compared to the conventional ASKs, with the two-sided ASK outperforming the one-sided ASK by achieving a lower SEP.