New BER Expression of MPSK

Abstract

This paper provides a new, exact, and general expression involving 1-D and 2-D Q-functions for the bit error probability of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase-shift keying (MPSK) under additive white Gaussian noise (AWGN) and fading channels when Gray code bit mapping is employed. Regular patterns in the error probability expression of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> th bit are observed while developing the bit error rate (BER) expression. From these patterns, we then derive a new BER expression for the MPSK constellation.