Random Matrices in Wireless Communication

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Despite very strong economic incentives to approach the information theoretic limits of wireless channels, the state-of-the-art (typified by second generation cellular wireless)remains far from an efficient utilization of spectrum and power resources. Wireless channels are known to be particularly challenging from the standpoint of analysis of fundamental limits. Fading, multiuser interference, and the space-distributed nature of wireless pose considerable difficulties. Relevant simple canonical models and theappreciation of the right mathematical tools are only emerging recently. The focus of this work is the investigation and application of a rich body of mathematical results that play a pivotal role in the analysis of wireless communication channels of contemporary interest. Random matrices are ubiquitous in the study of wireless systems. For example, fading makes channel coefficients random and time-varying, spreading waveforms in nonorthogonal code-division multiple access systems are accurately modeled as being randomly selected, multiantenna transmitters/receivers in scattering environments give rise to channels described by random matrices.Both coded (Shannon capacity) and uncoded (bit-error-rate) performance turn out to be determined (in most cases) by the eigenvalues of certain random matrices. Frequently, those matrices are quite large as their dimensions grow linearly with parameters such as the number of users and signaling degrees of freedom.Many information theoretic problems for which numerical simulation is the only alternativewith finite size matrices find elegant deterministic solutions in the infinite-size limit.This project is a systematic study of the spectrum of random matrices arising in single- and multiuser communication and information theory. Its results should influence the choice of both multiaccess techniques and receiver designs, as well as guide the development of asymptotic random matrix theory withtechnologically relevant problems.