Optimal 4-Ary Imbalanced-Phase-Amplitude Modulation in Uncorrelated and Correlated Receive Diversity PLC Systems Under Nakagami-$m$ Noise Environment

A receive diversity power line communication (PLC) system subject to correlated multipath channel fading and corrupted by additive Nakagami-
$m$
background noise is considered. The optimal receiver employing a 4-ary imbalanced-phase-amplitude modulation (I-PAM) scheme for data transmission is obtained, using which closed form expressions for the symbol error probability (SEP) in the union bound sense and the SEP in the asymptotic sense at high signal-to-noise ratio (SNR) are derived. The diversity order of the system is found to be independent of the shape parameter of the additive noise. Furthermore, the optimal 4-ary I-PAM constellation minimizing the SEP at lower SNR values is computed numerically. The optimal 4-ary I-PAM constellation is found to be elliptical in shape as opposed to the traditional circular QPSK constellation generally employed in wireless communication systems. The effects of the correlation among the multipath channel gains and the shape parameter of the noise on the optimality of the considered constellation are also presented via numerical studies.