New Expression for the SER of M-ary PSK

Dongweon YOON  

IEICE TRANSACTIONS on Communications   Vol.E88-B   No.4   pp.1672-1676
Publication Date: 2005/04/01
Online ISSN: 
DOI: 10.1093/ietcom/e88-b.4.1672
Print ISSN: 0916-8516
Type of Manuscript: LETTER
Category: Transmission Systems and Transmission Equipment for Communications
symbol error probability,  MPSK,  digital communications,  

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This letter derives a new exact and general closed-form expression involving a two-dimensional joint Gaussian Q-function for the symbol error rate (SER) of M-ary Phase Shift Keying (MPSK) under an additive white Gaussian noise (AWGN) channel. By using two rotations of coordinates the correlation coefficient between two Gaussian random vectors is provided, then with the derived correlation coefficient that characterizes the two-dimensional joint Gaussian Q-function, a new expression for the SER of MPSK is presented. The derived new SER expression offers a convenient method to evaluate the performances of MPSK for various cases of practical interest.