Asymptotics of Transmit Antenna Selection: Impact of Multiple Receive Antennas

Consider a fading Gaussian MIMO channel with $N_\mathrm{t}$ transmit and $N_\mathrm{r}$ receive antennas. The transmitter selects $L_\mathrm{t}$ antennas corresponding to the strongest channels. For this setup, we study the distribution of the input-output mutual information when $N_\mathrm{t}$ grows large. We show that, for any $N_\mathrm{r}$ and $L_\mathrm{t}$, the distribution of the input-output mutual information is accurately approximated by a Gaussian distribution whose mean grows large and whose variance converges to zero. Our analysis depicts that, in the large limit, the gap between the expectation of the mutual information and its corresponding upper bound, derived by applying Jensen's inequality, converges to a constant which only depends on $N_\mathrm{r}$ and $L_\mathrm{t}$. The result extends the scope of channel hardening to the general case of antenna selection with multiple receive and selected transmit antennas. Although the analyses are given for the large-system limit, our numerical investigations indicate the robustness of the approximated distribution even when the number of antennas is not large.