RIS-Assisted Noncoherent Wireless System: Error Analysis with Optimal Receiver and Multi-level ASK

This paper considers a reconfigurable intelligent surface (RIS) aided wireless communication system where the transmitter employs one-sided amplitude-shift keying (ASK) for data modulation and the receiver employs an optimal noncoherent maximum-likelihood rule for symbol detection. A novel statistical analysis is presented to approximate the weighted sum of a central and a non-central chi-squared random variable, which is used to derive a novel closed-form expression for the symbol error probability (SEP) of the noncoherent system. Furthermore, an optimization problem to minimize the system's SEP under transmission energy constraint is proposed, and novel algorithms are presented to obtain the optimal ASK constellation minimizing the SEP. Numerical results indicate that the noncoherent system achieves superior error performance and higher diversity order with the optimal ASK constellation compared to the traditional equispaced ASK constellation. Further, the optimal ASK significantly differs from the traditional one, with the difference becoming significant with an increase in the average signal-to-noise ratio and at a lower number of RIS's reflecting elements.