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

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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 languageEnglish
Title of host publicationProceedings of ISCCSP 2014
PublisherIEEE
Publication date2014
Pages384-387
ISBN (Print)978-1-4799-2890-3
DOIs
Publication statusPublished - 2014
Event6th International Symposium on Communications, Control, and Signal Processing - University of Athens, Athens, Greece
Duration: 21 May 201423 May 2014

Conference

Conference6th International Symposium on Communications, Control, and Signal Processing
LocationUniversity of Athens
CountryGreece
CityAthens
Period21/05/201423/05/2014

Keywords

  • MIMO
  • QAM
  • Constellation shaping

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