On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint

Alex Dytso; Luca Barletta; Gerhard Kramer

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arXiv · 2401.17084

On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint

Alex Dytso·Luca Barletta·Gerhard Kramer

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Abstract

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.

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Alex Dytso, Luca Barletta, Gerhard Kramer. 2024-01-30. On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint. https://arxiv.org/abs/2401.17084

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