Optimal Signaling and Selection Verification for Single Transmit-Antenna Selection

In marked contrast with the ideal error-free feedback assumption that is common in the literature, practical systems are likely to have severely bandwidth-limited, error-prone feedback channels. We consider the scenario where feedback from the receiver is used by the transmitter to select the best antenna, out of many available antennas, for data transmission. Feedback errors cause the transmitter to select an antenna different from the one signaled by the receiver. We show that optimizing the signaling assignment, which maps the antenna indices to the feedback codewords, improves performance without introducing any additional redundancy. For a system that uses error-prone feedback to transmit quadrature-phase-shift-keying-modulated data from a single antenna selected from many available spatially correlated antennas, we derive closed-form approximations for the data symbol error probability for an arbitrary number of receive antennas. We use these to systematically find the optimal signaling assignments using a low-complexity algorithm. The optimal signaling is intimately coupled to how the receiver performs selection verification, i.e., how it decodes the data signal when, due to feedback errors, it does not always know which antenna was used for data transmission. We show that ignoring feedback errors at the receiver can lead to an unacceptable performance degradation, and develop optimal and suboptimal, blind and nonblind selection-verification methods. With a small side-information overhead, nonblind verification approaches the ideal perfect selection-verification performance