Wireless channels with multiple transmit/receive antennas are known to provide a high spectral efficiency both when the channel is known to the receiver, and when the channel is not known to the receiver if the signal-to-noise ratio (SNR) is high. Here we analyze such systems at low SNR, which may find application in sensor networks and other low-power devices. The key point is that, since channel estimates are not reliable, it is often not reasonable to assume that the channel is known at the

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... eceiver at low SNR. In this unknown channel case, we show that for sensible input distributions, in particular all practical modulation schemes, the capacity is asymptotically quadratic in the SNR, , and thus much less than the known channel case where it exhibits a linear growth in . We show that under various signaling constraints, e.g., Gaussian modulation, unitary space-time modulation, and peak constraints, that mutual information is maximized by using a single transmit antenna. We also show that at low SNR, sending training symbols leads to a rate reduction in proportion to the fraction of training duration time so that it is best not to perform training. Furthermore, we show that the per-channel use mutual information is linear in both the number of receive antennas and the channel coherence interval. Index Terms-Low-signal-to-noise ratio (SNR) regime, multiple-antenna systems, noncoherent channels, Rayleigh fading. Institute of Technology,