Effect of Feedback Errors on Quantized Equal Gain Transmission

In this paper, we consider multiple-input, single-output (MISO) systems with per-antenna constrained beamforming at the transmitter, also known as equal gain transmission (EGT). The i.i.d. Rayleigh flat fading channel is assumed known to the receiver, and is quantized and sent to the transmitter through through a noisy finite-rate feedback channel. We model the noisy feedback channel as a symmetric error channel (i.e.,a channel where all index errors are equally likely), and analyze the effect of feedback channel errors on the performance of quantized EGT systems. It is found that the asymptotic performance (as the number of quantized codepoints gets large) of EGT with quantized feedback via a noisy channel depends on the channel behavior as the number of quantized points increase. It turns out that the binary symmetric channel (BSC) with random index assignment is a special case of the analysis, and the asymptotic performance approaches that of random beamforming. The accuracy of the expressions obtained are further verified through Monte Carlo simulations.