Factorization properties of the optimal signaling distribution of multi-dimensional QAM constellations

Metodi Plamenov Yankov; Søren Forchhammer; Knud J. Larsen; Lars P. B.  Christensen

doi:10.1109/ISCCSP.2014.6877894

Factorization properties of the optimal signaling distribution of multi-dimensional QAM constellations

Metodi Plamenov Yankov, Søren Forchhammer, Knud J. Larsen, Lars P. B. Christensen

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Abstract

In this work we study the properties of the optimal Proba- bility Mass Function (PMF) of a discrete input to a general Multiple Input Multiple Output (MIMO) channel. We prove that when the input constellation is constructed as a Cartesian product of 1-dimensional constellations, the optimal PMF factorizes into the product of the marginal 1D PMFs. This confirms the conjecture made in [1], which allows for optimizing the input PMF efficiently when the rank of the MIMO channel grows. The proof is built upon the iterative Blahut-Arimoto algorithm. We show that if the initial PMF is factorized, the PMF on each successive step is also factorized. Since the algorithm converges to the optimal PMF, it must therefore also be factorized

Original language	English
Title of host publication	Proceedings of ISCCSP 2014
Publisher	IEEE
Publication date	2014
Pages	384-387
ISBN (Print)	978-1-4799-2890-3
DOIs	https://doi.org/10.1109/ISCCSP.2014.6877894
Publication status	Published - 2014
Event	6th International Symposium on Communications, Control, and Signal Processing - University of Athens, Athens, Greece Duration: 21 May 2014 → 23 May 2014

Conference

Conference	6th International Symposium on Communications, Control, and Signal Processing
Location	University of Athens
Country/Territory	Greece
City	Athens
Period	21/05/2014 → 23/05/2014

Keywords

MIMO
QAM
Constellation shaping

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10.1109/ISCCSP.2014.6877894

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title = "Factorization properties of the optimal signaling distribution of multi-dimensional QAM constellations",

abstract = "In this work we study the properties of the optimal Proba- bility Mass Function (PMF) of a discrete input to a general Multiple Input Multiple Output (MIMO) channel. We prove that when the input constellation is constructed as a Cartesian product of 1-dimensional constellations, the optimal PMF factorizes into the product of the marginal 1D PMFs. This confirms the conjecture made in [1], which allows for optimizing the input PMF efficiently when the rank of the MIMO channel grows. The proof is built upon the iterative Blahut-Arimoto algorithm. We show that if the initial PMF is factorized, the PMF on each successive step is also factorized. Since the algorithm converges to the optimal PMF, it must therefore also be factorized",

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author = "Yankov, {Metodi Plamenov} and S{\o}ren Forchhammer and Larsen, {Knud J.} and Christensen, {Lars P. B.}",

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AU - Larsen, Knud J.

AU - Christensen, Lars P. B.

PY - 2014

Y1 - 2014

N2 - In this work we study the properties of the optimal Proba- bility Mass Function (PMF) of a discrete input to a general Multiple Input Multiple Output (MIMO) channel. We prove that when the input constellation is constructed as a Cartesian product of 1-dimensional constellations, the optimal PMF factorizes into the product of the marginal 1D PMFs. This confirms the conjecture made in [1], which allows for optimizing the input PMF efficiently when the rank of the MIMO channel grows. The proof is built upon the iterative Blahut-Arimoto algorithm. We show that if the initial PMF is factorized, the PMF on each successive step is also factorized. Since the algorithm converges to the optimal PMF, it must therefore also be factorized

AB - In this work we study the properties of the optimal Proba- bility Mass Function (PMF) of a discrete input to a general Multiple Input Multiple Output (MIMO) channel. We prove that when the input constellation is constructed as a Cartesian product of 1-dimensional constellations, the optimal PMF factorizes into the product of the marginal 1D PMFs. This confirms the conjecture made in [1], which allows for optimizing the input PMF efficiently when the rank of the MIMO channel grows. The proof is built upon the iterative Blahut-Arimoto algorithm. We show that if the initial PMF is factorized, the PMF on each successive step is also factorized. Since the algorithm converges to the optimal PMF, it must therefore also be factorized

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KW - Constellation shaping

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DO - 10.1109/ISCCSP.2014.6877894

M3 - Article in proceedings

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BT - Proceedings of ISCCSP 2014

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T2 - 6th International Symposium on Communications, Control, and Signal Processing

Y2 - 21 May 2014 through 23 May 2014

ER -

Factorization properties of the optimal signaling distribution of multi-dimensional QAM constellations

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