Performance Analysis and Optimization of Multi-Level ASK Constellation in a Receive Diversity Noncoherent PLC System

A receive diversity powerline communication system subject to uncorrelated Rayleigh distributed channel gains and corrupted by background noise modeled by Nakagami-m distribution is considered in this paper. For the transmitter utilizing multi-level amplitude-shift keying (ASK) modulation for data transmission and the receiver employing the optimal noncoherent decision rule for symbol estimation, the closed-form expression for the symbol error probability (SEP) of the system with an even number of diversity branches is derived using the union bound approach. Further, the constrained optimization problem for obtaining the optimal ASK signaling levels minimizing the SEP of the system with constrained total energy at the transmitter is formulated and solved numerically. It is observed that the optimal ASK constellation thus obtained outperforms the traditional equally-spaced ASK constellation for higher values of signal-to-noise ratio and diversity branches and at lower values of the shape parameter of the noise.