Performance analysis of transmit beamforming for MISO systems with imperfect feedback

In this paper, we analyze the performance of transmit beamforming on multiple-antenna Rayleigh fading channels with imperfect channel feedback. We characterize the feedback imperfections in terms of noisy channel estimation, feedback delay, and finite-rate channel quantization. We develop a general framework, that is valid for an arbitrary two-dimensional linear modulation, to capture the aforementioned imperfections and derive the symbol and bit error probability expressions for both M-PSK and M-ary rectangular QAM constellations with Gray code mapping. We show that the proposed analytical formulation is valid for a frequency-domain duplexing system with/without finite-rate channel quantization and a time-domain duplexing system. We validate the accuracy of the analysis through simulations, and assess the relative effects of channel estimation inaccuracy, feedback delay, and finite-rate quantization on the symbol and bit error performances for various constellations.