Optimal M-Level Two-Sided ASK for Noncoherent SIMO Wireless Systems in a Rician Fading Environment

This letter presents a noncoherent single input multiple output wireless communication system, in which the transmitter utilizes a multi-level two-sided amplitude shift keying (ASK) modulation scheme to transmit data symbols over statistically independent Rician fading channels. The receiver applies a maximum likelihood detector to decode the received data. For the performance assessment of such a system, a series-form expression for the union bound on symbol error probability (SEP) is derived and a closed-form expression for the SEP is obtained by applying the central limit theorem when the number of receive antennas is sufficiently large. Moreover, an optimization framework is introduced to obtain optimal ASK constellation, minimizing the SEP under an average transmit energy constraint. The superior performance of the system in comparison with the traditional two-sided ASK constellation is corroborated via numerical results under various parameter configurations.