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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.

In this paper, we consider a receive diversity wireless communication system with the transmitter employing multi-level amplitude-shift keying (ASK) signaling scheme for data modulation over Rician fading channels and the receiver utilizing an optimal non-coherent maximum likelihood detector for data reception. The system's performance is analyzed in terms of deriving the series-form expression of the union bound on the symbol error probability (SEP) using the pairwise error probability expressions and the proposed optimal detection rule. Furthermore, the union-bound on the SEP of the system is proposed to be minimized by deriving an optimal multi-level ASK constellation under the constraint of total available energy at the transmitter. Numerical results show the superior performance of the considered communication system with optimal ASK constellation set compared to the traditional equally-spaced ASK constellation. Furthermore, it is observed that higher values of the Rician factor of the system, the average SNR, and the number of receive diversity branches play a crucial role in the reliability of the wireless communication system.