Combining Beamforming and Space-Time Coding Using Noisy Quantized   Feedback
  The goal of combining beamforming and space-time coding in this work is to obtain full-diversity order and to provide additional received power (array gain) compared to conventional space-time codes. In our system, we consider a quasi-static fading environment and we incorporate both high-rate and low-rate feedback channels with possible feedback errors. To utilize feedback information, a class of code constellations is proposed, inspired from orthogonal designs and precoded space-time block codes, which is called generalized partly orthogonal designs or generalized PODs. Furthermore, to model feedback errors, we assume that the feedback bits go through binary symmetric channels (BSCs). Two cases are studied: first, when the BSC bit error probability is known a priori to the transmission ends and second, when it is not known exactly. In the first case, we derive a minimum pairwise error probability (PEP) design criterion for generalized PODs. Then we design the quantizer for the erroneous feedback channel and the precoder codebook of PODs based on this criterion. The quantization scheme in our system is a channel optimized vector quantizer (COVQ). In the second case, the design of the quantizer and the precoder codebook is based on similar approaches, however with a worst-case design strategy. The attractive property of our combining scheme is that it converges to conventional space-time coding with low-rate and erroneous feedback and to directional beamforming with high-rate and error-free feedback. This scheme shows desirable robustness against feedback channel modeling mismatch. 
Siavash Ekbatani and Hamid Jafarkhani