  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.
