Comments on “Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels

Seong Ho Chae and Hoojin Lee

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10.23919/JCN.2021.000017

Abstract :In the paper “Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels” of Wang et al. [1], they derived the algebraic formulas of upper- and lower- bounds for the average symbol error probability (ASEP) of M-ary phase shift keying (M-PSK) in a class of composite fading channels by using mixture gamma (MG) distribution, which is based on the assumption of the lack of closed-form expression for exact ASEP. However, the exact ASEP can be represented in closed-form by utilizing hypergeometric functions. Therefore, in this paper, we formulate the closed-form formulas of the exact and asymptotic ASEPs for general M-PSK in a class of the composite fading channels over MG distribution. We present some numerical results to validate our derived analytical results. 

Index terms :M-ary phase shift keying, mixture gamma distribution, symbol error probability