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.

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.