On2 × 2MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint

A multi-input multi-output (MIMO) Gaussian channel with two transmit antennas and two receive antennas is studied that is subject to an input peak-power constraint. The capacity and the capacity-achieving input distribution are unknown in general. The problem is shown to be equivalent to a channel w...

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Bibliographic Details
Main Authors Dytso, Alex, Barletta, Luca, Kramer, Gerhard
Format Journal Article
LanguageEnglish
Published 30.01.2024
Subjects
Computer Science - Information Theory
Mathematics - Information Theory
Online AccessGet full text
DOI10.48550/arxiv.2401.17084

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Summary:A multi-input multi-output (MIMO) Gaussian channel with two transmit antennas and two receive antennas is studied that is subject to an input peak-power constraint. The capacity and the capacity-achieving input distribution are unknown in general. The problem is shown to be equivalent to a channel with an identity matrix but where the input lies inside and on an ellipse with principal axis length$r_p$and minor axis length$r_m$ . If$r_p \le \sqrt{2}$ , then the capacity-achieving input has support on the ellipse. A sufficient condition is derived under which a two-point distribution is optimal. Finally, if$r_m < r_p \le \sqrt{2}$ , then the capacity-achieving distribution is discrete.
DOI:10.48550/arxiv.2401.17084