Asymptotic Capacity Gain of Transmit Antenna Selection

Antenna selection provides a low-cost low complexity solution for MIMO systems, in particular transmit antenna selection exploits partial knowledge of the channel that can be made available without excessive feedback bandwidth. In this work we explore information theoretic limits of transmit antenna selection for high SNR and large number of transmit antennas. We define the capacity gain as the constant term in the asymptotic expansion of the ergodic capacity with respect to the SNR. We show that this value is directly related to the channel state information (CSI) at the transmitter. We compute and investigate the asymptotic behavior of the capacity gain for three cases: where the transmitter has complete CSI, no CSI, and partial CSI (antenna selection). We show that while water-filling provides a capacity gain that increases logarithmically in M (the number of transmit antennas), the capacity gain of transmit antenna selection behaves only like log(log(M)).