Optimal Fractional Pilot Duration for a Correlated Receive Diversity Reliable PLC System With Imperfect CSI in Nakagami-m Noise Environment

The paper presents a single-input-multiple-output-based power line communication (PLC) system employing <inline-formula> <tex-math notation="LaTeX">${M}$ </tex-math></inline-formula>-ary phase-shift keying signaling for data transmission, with the channels subjected to correlated Rayleigh multipath channels and corrupted by Nakagami-<inline-formula> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> noise environment. The channel state information for the PLC system is obtained prior to data transmission using the minimum mean square error estimation technique, utilizing which a maximum likelihood-based sub-optimal receiver is proposed. The closed-form expression for the symbol error probability (SEP) is derived, for the cases of the channels following exponential and uniform correlations, using a characteristic function approach. Furthermore, the optimal pilot symbol duration is obtained to maximize the normalized error-free data rate of the system, which simultaneously saves on the energy of the pilot symbols and reduces the SEP of the data symbols. The numerical results demonstrate the effect of variation of different system parameters such as signal-to-noise ratio, channel diversity, pilot symbol quality, correlation factor, and the noise shape parameter <inline-formula> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> of the background noise on the maximum normalized error-free data rate and thereby providing various insights into the system design for a reliable and energy-efficient PLC system with imperfect knowledge of the channels at the receiver.