## Abstract

We investigate the capacity loss of 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 robust input also when the noise is not Gaussian. Specifically, we show that for n_{t} transmit antennas and n _{r} receive antennas, the capacity loss of i.i.d Gaussian input is smaller than min{n_{t}/2, n_{r}/2, log_{2}(1 + n _{t}/n_{r})} 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: n_{r}/2 log_{2}(n_{t}/n_{r}) bits for 1 ≤ n_{r} ≤ n_{t}/e and n_{t}i/2 log_{2}(e)/e bits for n_{r} ≥ n_{t}/e.

Original language | English |
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Pages | 227-229 |

Number of pages | 3 |

State | Published - 2004 |

Event | 2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings - Tel-Aviv, Israel Duration: 6 Sep 2004 → 7 Sep 2004 |

### Conference

Conference | 2004 23rd IEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings |
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Country/Territory | Israel |

City | Tel-Aviv |

Period | 6/09/04 → 7/09/04 |