TY - JOUR

T1 - On the Capacity of the Peak Power Constrained Vector Gaussian Channel

T2 - An Estimation Theoretic Perspective

AU - Dytso, Alex

AU - Al, Mert

AU - Poor, H. Vincent

AU - Shamai Shitz, Shlomo

N1 - Funding Information:
Manuscript received April 23, 2018; revised September 16, 2018; accepted December 5, 2018. Date of publication January 1, 2019; date of current version May 20, 2019. This work was supported in part by the U.S. National Science Foundation under Grant CCF–1513915 and in part by the European Union’s Horizon 2020 Research and Innovation Programme under Grant 694630. This paper was presented in part in [37].
Funding Information:
This work was supported in part by the U.S. National Science Foundation under Grant CCF-1513915 and in part by the European Union's Horizon 2020 Research and Innovation Programme under Grant 694630.
Publisher Copyright:
© 1963-2012 IEEE.

PY - 2019/6

Y1 - 2019/6

N2 - This paper studies the capacity of an n -dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius R centered at the origin. It is known that in this setting, the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions, and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint R, such that the input distribution supported on a single sphere is optimal. The maximum Rn, such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that Rn scales as √ n and the exact limit of Rn√n is found.

AB - This paper studies the capacity of an n -dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius R centered at the origin. It is known that in this setting, the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions, and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint R, such that the input distribution supported on a single sphere is optimal. The maximum Rn, such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that Rn scales as √ n and the exact limit of Rn√n is found.

KW - Capacity

KW - I-MMSE

KW - amplitude constraint

KW - harmonic functions

KW - minimum mean square error (MMSE)

KW - mutual information

KW - peak-power

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U2 - 10.1109/TIT.2018.2890208

DO - 10.1109/TIT.2018.2890208

M3 - Article

AN - SCOPUS:85065971042

SN - 0018-9448

VL - 65

SP - 3907

EP - 3921

JO - IRE Professional Group on Information Theory

JF - IRE Professional Group on Information Theory

IS - 6

M1 - 8598797

ER -