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Entropy 2019, 21(2), 200; https://doi.org/10.3390/e21020200

Amplitude Constrained MIMO Channels: Properties of Optimal Input Distributions and Bounds on the Capacity

1
Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
2
Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
*
Authors to whom correspondence should be addressed.
Parts of the material in this paper were presented at the 2017 IEEE Global Communications Conference (Singapore, 4–8 December 2017).
Received: 21 January 2019 / Revised: 6 February 2019 / Accepted: 13 February 2019 / Published: 19 February 2019
(This article belongs to the Special Issue Information Theory for Data Communications and Processing)
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Abstract

In this work, the capacity of multiple-input multiple-output channels that are subject to constraints on the support of the input is studied. The paper consists of two parts. The first part focuses on the general structure of capacity-achieving input distributions. Known results are surveyed and several new results are provided. With regard to the latter, it is shown that the support of a capacity-achieving input distribution is a small set in both a topological and a measure theoretical sense. Moreover, explicit conditions on the channel input space and the channel matrix are found such that the support of a capacity-achieving input distribution is concentrated on the boundary of the input space only. The second part of this paper surveys known bounds on the capacity and provides several novel upper and lower bounds for channels with arbitrary constraints on the support of the channel input symbols. As an immediate practical application, the special case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap to the capacity if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the regime of high amplitudes, it is shown that the capacity scales linearly with the minimum between the number of transmit and receive antennas, similar to the case of average power-constrained inputs. View Full-Text
Keywords: MIMO; channel capacity; amplitude constraint; input distrbution; capacity bounds MIMO; channel capacity; amplitude constraint; input distrbution; capacity bounds
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Dytso, A.; Goldenbaum, M.; Poor, H.V.; Shamai (Shitz), S. Amplitude Constrained MIMO Channels: Properties of Optimal Input Distributions and Bounds on the Capacity. Entropy 2019, 21, 200.

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