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The capacity loss of uncorrelated equi-power Gaussian input over MIMO channel

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2 Author(s)
Philosof, T. ; Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Israel ; Zamir, R.

We investigate the capacity loss of an uncorrelated Gaussian input with equal power (i.i.d. Gaussian input) over a multi-input multi-output linear additive noise (not necessarily Gaussian nor memoryless) channel. Previous work showed that this input is the best input in the case of Gaussian noise, assuming the channel matrix is known at the receiver but unknown at the transmitter. We show that i.i.d. Gaussian is a robust input also when the noise is not Gaussian. Specifically, we show that for nt transmit antennas and nr receive antennas, the capacity loss of an i.i.d. Gaussian input is smaller than min{nt/2, (nr/2)log2(1 + nt/nr)} bits, for any noise and channel matrix. This bound is apparently not tight. Nevertheless, for the case of Gaussian noise we derive a stronger bound which is tight for a "critical" channel matrix: (nr/2)log2(nt/nr) bits for 1≤ nr≤(nt/e) and (nt/2)(log2(e))/e bits for nr≥(nt/e).

Published in:

Electrical and Electronics Engineers in Israel, 2004. Proceedings. 2004 23rd IEEE Convention of

Date of Conference:

6-7 Sept. 2004