Asymptotic Capacity Analysis of Transmit Antenna Selection

 
It is known that antenna selection provides a low-cost low complexity
solution for MIMO systems.  Transmit antenna selection improves the
capacity without need for excessive amounts of feedback, thus it is
attractive especially for cases where feedback rate for channel state
information is limited.  In this work we explore the information
theoretic limits of transmit antenna selection for high SNR and large
number of transmit antennas. To do so, we take a fresh look at the
role of channel state information at the transmitter. We define the
capacity gain as the constant term in the asymptotic expansion of the
ergodic capacity with respect to the signal-to-noise ratio (SNR).

We show that the channel state information (CSI) at transmitter
improves the capacity gain, but does not improve the growth
rate. Since the growth rate is not affected by CSI, it follows that
the quality of any method that uses CSI at the transmitter must be
measured by the capacity gain. We compute the capacity gains with and
without CSI for MIMO channels, and investigate the behavior of
capacity gain for both cases in the asymptote of large number of
transmit antennas.

For transmit antenna selection, we study the successive subspace
projection scheme, which has recently been shown to perform almost the
same as optimal selection. We derive a closed form analytical tight
upper bound for transmit selection and we use that to explore the
behavior of the capacity gain for large number of transmit
antennas. We show that, while water filling provides a capacity gain
which increases logarithmically in M (the number of transmit
antennas), the capacity gain of transmit antenna selection behaves
only like log(log(M)).

For Low SNR  case, we use the concept of channel gain, a measure
introduced by Verdu.  We show that  the channel gain for water-filling
capacity increases linearly in M, whereas for antenna selection it only
increases logarithmically in M..