Optimal Multi-Level ASK Modulations for RIS-Assisted Communications with Energy-Based Noncoherent Reception

This paper investigates the performance of one- and two-sided amplitude shift keying (ASK) modulations in noncoherent single-input single-output (SISO) wireless communication systems assisted by a reconfigurable intelligent surface (RIS). Novel noncoherent receiver structures are proposed based on the energy of the received symbol and the choice of the modulation scheme for data transmission. The system's performance is assessed in terms of the symbol error rate (SER) and an optimization framework is proposed to determine the most effective one- and two-sided ASKs to minimize the SER, while adhering to average a transmit power constraint. Two scenarios based on the availability of the statistical characteristics of the wireless channel are explored: a) the transceiver pair has complete knowledge of the channel statistics, and b) both end nodes possess knowledge of the statistics of the channel gain up to its fourth moment, and novel algorithms are developed to obtain optimal ASKs for both of them. Extensive numerical evaluations are presented showcasing that there exists a threshold signal-to-noise ratio (SNR) above which the optimal ASKs outperform the traditional equispaced ASKs. The dependencies of the SER performance and the SNR threshold on various system parameters are assessed, providing design guidelines for RIS-assisted noncoherent wireless communication systems with multi-level ASK modulations.