Comments on "tight bounds and invertible average error probability expressions over composite fading channels"

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.