Pseudo-Gray Coding for Beamforming Systems

In a multiple-input multiple-output (MIMO) beam- forming system with finite rate feedback, the receiver sends back quantized channel information to the transmitter via a feedback channel. The overall system performance is degraded due to feedback errors. In this paper, we treat the feedback of the beamforming vector as a generalized vector quantizer (VQ), and adopt index assignment (IA) technique to cope with feedback errors. A lower bound to the average symbol error rate (SER) is derived, and an IA design criterion is proposed to minimize this bound, which is in accord with the pseudo-Gray coding principle in conventional IA design literature. Numerical results show that well-designed IA schemes improve the SER considerably.