Performance Bound Analysis on Transmit Antennas Selection Systems Considering Erroneous Channel Information

We consider multiple-inputs-single-output (MISO) systems equipped with N transmit and single receive antennas, and concentrate on transmit antenna selection (TAS) for flat Rayleigh fading channels. We assume perfect channel state information (CSI) at receiver and imperfect CSIs through an feedback link at transmitter. The metric of TAS are those with the largest instantaneous signal-to- noise ratio (SNR), the best 2 out of N available transmit antennas always are selected. We use Alamouti encoding scheme and derive the probability density function (PDF) of Frobenius norm of column vector of the channel matrix. Using the known PDF we can derive the joint PDF of order statistics channel for the subseti, j. Assuming that the transmitted signals employ Mary phase-shift keying (MPSK) constellation, we consider the impact of imperfect antenna selection subsets on system performance, and explicitly derive a closed-form BER expression of Chernoff upper bounds (CUB). For two special cases with 2 out of N =3 and 4 possible transmit antennas, we analyses asymptotic performance of selected subsets. Numerical and simulating results show that we can achieve full spatial diversity with antenna selection in the presence of imperfect CSI and the largest ordinal number antenna selected as if all the transmit antennas were used; there may be some loss in the diversity order without the best transmit antenna.