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Unitary Integrations for Unified MIMO Capacity and Performance Analysis Open Access


Other title
MIMO capacity
Character expansion
Gaussian random matrix
Wishart matrix
Unitary integration
Type of item
Degree grantor
University of Alberta
Author or creator
Ghaderipoor, Alireza
Supervisor and department
Tellambura, Chintha (Electrical and Computer Engineering)
Examining committee member and department
Department of Electrical and Computer Engineering

Date accepted
Graduation date
Doctor of Philosophy
Degree level
Integrations over the unitary group are required in many applications including the joint eigenvalue distributions of the Wishart matrices. In this thesis, a universal integration framework is proposed to use the character expansions for any unitary integral with general rectangular complex matrices in the integrand. The proposed method is applied to solve some of the well--known but not solved in general form unitary integrals in their general forms, such as the generalized Harish--Chandra--Itzykson--Zuber integral. These integrals have applications in quantum chromodynamics and color--flavor transformations in physics. The unitary integral results are used to obtain new expressions for the joint eigenvalue distributions of the semi--correlated and full--correlated central Wishart matrices, as well as the i.i.d. and uncorrelated noncentral Wishart matrices, in a unified approach. Compared to the previous expressions in the literature, these new expressions are much easier to compute and also to apply for further analysis. In addition, the joint eigenvalue distribution of the full--correlated case is a new result in random matrix theory. The new distribution results are employed to obtain the individual eigenvalue densities of Wishart matrices, as well as the capacity of multiple--input multiple--output (MIMO) wireless channels. The joint eigenvalue distribution of the i.i.d. case is used to obtain the largest eigenvalue density and the bit error rate (BER) of the optimal beamforming in finite--series expressions. When complete channel state information is not available at the transmitter, a codebook of beamformers is used by the transmitter and the receiver. In this thesis, a codebook design method using the genetic algorithm is proposed, which reduces the design complexity and achieves large minimum--distance codebooks. Exploiting the specific structure of these beamformers, an order and bound algorithm is proposed to reduce the beamformer selection complexity at the receiver side. By employing a geometrical approach, an approximate BER for limited feedback beamforming is derived in finite--series expressions.
License granted by Alireza Ghaderipoor ( on 2009-10-01T21:38:03Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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