0018-9545 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.2966796, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2020 1 Performance Analysis of Coherent PLC with MPSK Signaling in Nakagami-m Noise Environment Soumya P. Dash, Member, IEEE, Ranjan K. Mallik, Fellow, IEEE, and Saif Khan Mohammed, Senior Member, IEEE Abstract—An N -branch receive diversity power line commu- nication (PLC) system subject to Rayleigh fading and corrupted by additive Nakagami-m background noise is considered. A sub- optimal maximal-ratio-combining (MRC), an optimal diversity combining, and a Gauss-optimal receiver are proposed for the PLC system. A closed form expression for the exact symbol error probability (SEP) and a union bound SEP expression are obtained for the proposed MRC and Gauss-optimal receivers, respectively, using a characteristic function (c.f.) approach for the system employing M-ary phase-shift keying (MPSK) at the transmitter, conditioned to mN being an integer. The asymptotic expression for the SEP obtained for the MRC receiver at high signal-to-noise (SNR) demonstrates that the diversity order of the system is independent of the shape parameter m of the additive noise which is identical to the diversity order of the optimal and the Gauss-optimal receivers. Further, numerical studies justify the advantages of employing receive diversity to achieve superior SEP performance. The effect of increasing the diversity branches on the PLC system performance with varying m and the power efficiency of the PLC system are also presented. Index Terms—Characteristic function, M-ary phase-shift key- ing (MPSK), Nakagami-m noise, power line communication (PLC), receive diversity, symbol error probability (SEP). I. I NTRODUCTION Power line communication (PLC) technology has gained increased attention for indoor and outdoor applications related to smart grid, home automation systems, and providing inter- net and local area network services to offices and houses [1], [2]. Moreover, in recent times, the applications of PLC have also been envisaged and demonstrated for transportation and other automotive services. Such applications include lightening the cable bundles for electronic control in vehicles, high- speed entertainment systems in multimedia buses, activation of actuators in low-speed data buses, data transfers in vehicle trains, and installation of new electrical devices in cars [3], [4]. Moreover, employment of PLC technology in vehicular applications ensures reduction in complexity, cost, weight of the wiring harness, and fuel consumption of the vehicles, owing to the pre-existing power line network and low instal- lation costs in various vehicles [5]. The main challenge in the successful implementation of the PLC technology is attributed Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. Soumya P. Dash is with the School of Electrical Sciences, Indian Insti- tute of Technology - Bhubaneswar, Argul, Khordha 752050, India (e-mail: soumyapdashiitbbs@gmail.com). Ranjan. K. Mallik, and Saif Khan Mohammed are with the Depart- ment of Electrical Engineering, Indian Institute of Technology - Delhi, Hauz Khas, New Delhi 110016, India (e-mail: rkmallik@ee.iitd.ernet.in, saifkmohammed@gmail.com). to the unconventional nature of the PLC channel which leads to unreliable transmission of data via such channels. Thus, efficient design of transceivers becomes essential for executing reliable PLC systems in practice [6]. Unlike traditional wired communication systems, the trans- mission errors in PLC systems occur due to the multipath fading phenomenon and the additive noise corrupting the channel. The statistical model of the multipath phenomenon in PLC systems has been found to be site dependent and is presented accordingly in the literature. Many of such power lines networks experimentally validate the occurrence of Rayleigh distribution to model the multipath statistics. The measured peak and notch widths of the transfer function in the 30 kHz to 100 MHz frequency band for indoor PLC channel environments is found to follow the Rayleigh distribution [7]. The multiple arrival paths of the PLC channel over a bandwidth of 30 MHz studied in [8] and the transmission path between the source and destination for a three node PLC network interconnected with a main NAYY150SE power cable via NAYY50SE house connection cables studied in [9] are also found to follow the Rayleigh distribution. The amplitude distribution in the presence of multiple scattering points in a train automation and mass transmit systems is also modeled by a Rayleigh distribution [10]. This distribution has also been justified for other system models in [11], [12]. The additive noise corrupting the PLC systems is mainly divided into background and impulsive noise. The background noise is always present in a PLC system and is mainly caused by the combinations of the noises generated by multiple sources consuming low power in the system. Ingression of amplitude modulated signals in the PLC network is another major source of additive background noise corrupting the transmission of data symbols [13]. The experimental studies carried out in the frequency range of 1-30 MHz and presented in [14] statistically model the envelope of the background noise by the Nakagami-m distribution with m< 1. Some of the work already carried out in this area are presented in [6], [15]–[19]. In [6], the authors have carried the symbol error probability (SEP) analysis for an optimal receiver employing binary phase-shift keying (BPSK) modula- tion by considering the Hoyt approximation of the Nakagami- m additive noise. The authors in [15] have carried out the outage probability and bit error probability (BER) analysis for a PLC system with BPSK signaling scheme and corrupted by colored background noise. Further, the authors in [16] and [17] have considered a suboptimal receiver for a single channel PLC system and obtained the SEP expressions for the system with and without fading, respectively. Moreover, the