Optimal QPSK Constellation for a PLC System in Nakagami-m Noise Environment

This letter considers a single-input single-output powerline communication (PLC) system employing quadrature phase-shift keying (QPSK) modulation scheme under Rayleigh fading and Nakagami-m noise environment. The series form expression of the symbol error probability (SEP) for the system is derived by considering the QPSK constellation as a combination of two orthogonal binary phase-shift keying constellations. Moreover, the optimal QPSK constellation minimizing the SEP under the constraint of given average transmission power is obtained. It is observed that the optimal solution of the QPSK constellation is elliptical in shape as compared to the traditional circular QPSK constellation. Further studies on the shape of the optimal elliptical QPSK constellation with varying shape parameter of the additive noise are carried out by numerical studies.