On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911767833083904 |
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| author | Dytso, Alex Barletta, Luca Kramer, Gerhard |
| author_facet | Dytso, Alex Barletta, Luca Kramer, Gerhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint Dytso, Alex Barletta, Luca Kramer, Gerhard Information Theory 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. |
| title | On $2 \times 2$ MIMO Gaussian Channels with a Small Discrete-Time Peak-Power Constraint |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.17084 |