Performance analysis of scheduled transmit beamforming systems under non-identically delayed feedback channels

In this paper, we investigate the performance analysis of a scheduled transmit beamforming system under non-identically delayed feedback channels. This paper derives the exact closed-form expressions of the scheduling system for the symbol error rate (SER) with M-ary phase shift keying and quadrature amplitude modulation including the outage probability and ergodic capacity under the non-identical feedback delay channels. We also quantify the diversity order and signal to noise ratio (SNR) gain of the SER and outage probability which provide insights into which parameters affect the system performance. From analytical results, we show that the feedback delay in the scheduling system removes only the advantage of the spatial diversity not the advantage of multi-user diversity. Thus, the diversity order of the SER and outage probability for the scheduling system is proportional to the number of users under the non-identically delayed feedback channels. Further, the SNR gain of the SER and outage probability for the scheduling system is proportional to the sum of the feedback delay coefficient for all user terminals. Finally, the ergodic capacity of the proposed system is significantly improved as the number of users increases, while being relatively less affected by the sum of the feedback delay coefficients.