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Analysis of multiple antenna wireless links at low SNR

In the low signal-to-noise (SNR) regime when the channel is not known to both transmitter and receiver, we show that the capacity of a multiple antenna Rayleigh fading link is asymptotically quadratic in the SNR for all practical input distributions. This is much less than the known channel case where it exhibits a linear growth in the SNR. Under various signaling constraints we show that mutual information is maximized by using a single transmit antenna. Also sending training symbols offers no advantage at low SNR.