Optimal Multi-Level Amplitude-Shift Keying for Channel Norm-Based SIMO Wireless Communication System in Rician Fading Environment

Abstract

An N-branch receive diversity wireless system subject to prominent line-of-sight (LoS) fading in the multipath is considered in this paper. The fading channels are modeled by Rician distributions and the transmitter employs multi-level amplitude-shift keying (ASK) for data modulation. The receiver is assumed to possess the knowledge of the magnitude of the fading channels and thus, an optimal receiver structure based on the knowledge of the channel-norm is derived. Owing to the complexity of the receiver structure, two novel suboptimal receivers, inspired by the central limit theorem and Euclidean distance, are proposed. Furthermore, series-form expressions for the symbol error probability (SEP) for both these receivers are derived. This is followed by proposing and solving an optimization framework aimed at finding the optimal multi-level ASK constellations to minimize the SEP expressions obtained for the two receivers under an average system energy constraint. The analytical framework is verified by numerical studies that show the efficacy of the obtained optimal ASK constellations over the equally-spaced ASK constellations traditionally used for wireless systems. Moreover, it is observed that the traditional Euclidean distance-based receiver isn’t appropriate for optimal performance and the optimal factor $\alpha $ is dependent on the average signal-to-noise ratio and the number of diversity branches. Additionally, the dependencies of the shape of the optimal constellation schemes on the various system parameters are studied via numerical results. Thus, the proposed novel receivers and multi-level ASK schemes provide crucial design insights for reliable, hardware-efficient, and energy-efficient communication systems with prominent LoS links.