Antenna selection for space-time coded systems with imperfect channel estimation

This paper studies the performance of antenna selection (AS) for space-time (ST) coded systems with noisy channel estimates. For coherent AS systems over Rayleigh flat fading channels, we derive the pairwise error probability (PEP) in the presence of imperfect channel estimation, where the channel is estimated using training insertion and minimum mean square error (MMSE) estimation. Multiplexed training is employed, where the antennas are multiplexed to the small number of RF chains available in the AS system. AS is performed only at the receiver, using the maximum estimated channel power selection rule. Both the maximum likelihood (ML) decoder taking into account the channel estimation error, and the minimum distance decoder are considered, and full diversity gain is shown to be preserved for both cases. Based on the derived training-based PEP, the effective SNR and the coding gain loss due to training are quantified for square unitary and orthogonal codes. The optimal power allocation between the training and data symbols is obtained by minimizing the PEP. For AS systems employing orthogonal designs, we further derive the exact PEP expression in closed-form. We also show that when square unitary training is employed, AS using the norm of MMSE channel estimates is equivalent to AS using the norm (power) of the received signal. Exploiting this fact, we propose an alternate training scheme which avoids multiplexing, has higher spectral efficiency, and better performance compared to the multiplexed training scheme. Simulations are shown to validate our analysis.