On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint
Autor: | Dytso, Alex, Barletta, Luca, Kramer, Gerhard |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 8 pages, 1 figure. Submitted to IEEE ISIT 2024 |
Databáze: | arXiv |
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