Capacity of MIMO Channels With Antenna Selection

This correspondence studies the capacity of multiple-input-multiple-output (MIMO) channels in the presence of antenna selection. Antenna selection reduces the complexity of the radio devices and requires only a small amount of channel state feedback. For high signal-to-noise ratio (SNR), we define excess rate as the constant term in the expansion of the ergodic capacity in terms of SNR. It is shown that this value is representative of the channel state information (CSI) at the transmitter. The asymptotic behavior of the excess rate is then analyzed for three cases: complete CSI, no CSI, and partial CSI at transmitter (antenna selection). While water-filling provides a excess rate that increases logarithmically in M (the number of transmit antennas), the excess rate of transmit antenna selection behaves only like log(log M). For the low SNR case, we use the concept of channel gain, a measure introduced by Verdu. We show that channel gain for antenna selection increases only logarithmically in M as opposed to water-filling channel gain which increases linearly in M. The same techniques are also applied to the receive selection, and corresponding results are noted in high- and low-SNR regimes. The methodology developed in this correspondence, although motivated by antenna selection, is fairly general and can be used for any system where partial CSI is available at the MIMO transmitter.