Majorization and Matrix-Monotone Functions in Wireless Communications

Author(s): Eduard Jorswieck;Holger Boche

Source:
    Journal:Foundations and Trends® in Communications and Information Theory
    ISSN Print:1567-2190,  ISSN Online:1567-2328
    Publisher:Now Publishers
    Volume 3 Number 6,

Document Type: Article
Pages: 149(553-701)
DOI: 10.1561/0100000026

Abstract: This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions , reviews their basic definitions and describes their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. The techniques are applied to solve communication and information theoretic problems in wireless communications. The impact of spatial correlation in multiple antenna systems is characterized for many important performance measures, e.g., average mutual information, outage probability, error performance, minimum and wideband slope, zero-outage capacity, and capacity region. The impact of user distribution in cellular systems is characterized for different scenarios including perfectly informed transmitters and receivers, regarding, e.g., the average sum rate, the outage sum rate, maximum throughput. Finally, a unified framework for the performance analysis of multiple antenna systems is developed based on matrix-monotone functions. The optimization of transmit strategies for multiple antennas is carried out by optimization of matrix-monotone functions. The results within this framework resemble and complement the various results on optimal transmit strategies in single-user and multiple-user multiple-antenna systems.

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