Comments on “Error Performance of Transmit Beamforming With Delayed and Limited Feedback”

In the paper “Error Performance of Transmit Beamforming With Delayed and Limited Feedback” of Ma et al., they provided the analytical derivation of an accurate approximation for the symbol error rate (SER) of transmit beamforming (TB) systems employing M-ary phase-shift keying (M-PSK) in Rayleigh fading channels, considering the effect of delayed and limited-rate codebook index feedback. However, the derived formula is valid only for the binary phase-shift-keying (i.e., M = 2) modulation, which means that the formula is not general for the M-PSK modulations with M ≥ 2. Therefore, we aim at deriving the correct closed-form formula for the accurate approximation for the SER, which is validated through the numerical results. Furthermore, we also present the corresponding correct coding gain achieved by the TB system.