Asymptotic performance of space-time block codes with imperfect transmit antenna selection

Introduction: Space-time codes with antenna subset selection has been a subject of intense research recently [1–6]. In [1] and [4], the error performance of the Alamouti scheme with transmit antenna selection was investigated and it was shown that a full diversity order can be achieved, as if all the transmit antennas were used. In most of the published papers dealing with transmit antenna selection, it is assumed that the antenna subset which maximises the received signal-to-noise ratio (SNR), or, the best antenna subset, is selected for transmission. In practical scenarios, it is not feasible to assume that the best antenna subset can always be selected owing to channel estimation errors, feedback delay and feedback errors. Therefore, the impact of imperfect antenna subset selection on system performance should be investigated. The first effort in determining the effect of imperfect antenna selection policy on system performance appeared in [7] for a multipleinput-multiple-output (MIMO) system with a single transmit antenna selected for uncoded transmission and receiver maximal-ratio combining at the receiver. An interesting conclusion is reached that the system diversity order is proportional to the ordinal number of the selected antenna. In this Letter, the error performance of the Alamouti space-time block code (STBC) [8] with transmit antenna selection is investigated for imperfect antenna subset selection. It is observed that the system diversity order is proportional to the largest ordinal number of the antenna within the selected antenna subset.