Random Matrices in Wireless Communication

尽管有非常强的经济动机来接近无线信道的信息理论极限，但是现有技术（以第二代蜂窝无线为代表）仍然远远没有有效利用频谱和功率资源。 从分析基本限制的角度来看，无线信道是特别具有挑战性的。 衰落、多用户干扰和无线电的空间分布特性造成了相当大的困难。相关的简单规范模型和正确的数学工具的评价只是最近才出现的。 这项工作的重点是调查和应用的数学结果，发挥了关键作用，在分析无线通信信道的当代利益丰富的机构。 随机矩阵在无线系统的研究中是普遍存在的。 例如，衰落使得信道系数随机且时变，非正交码分多址系统中的扩频波形被精确地建模为随机选择的，散射环境中的多天线发射机/接收机产生由随机矩阵描述的信道。（香农容量）和未编码（误比特率）的性能（在大多数情况下）由某些随机矩阵的特征值决定。 通常，这些矩阵是相当大的，因为它们的维数随着参数（如用户数和信令自由度）线性增长。许多信息论问题，数值模拟是唯一的选择与有限大小的矩阵找到优雅的确定性解决方案在无限大小的限制。本项目是一个系统的研究随机矩阵的频谱产生在一个单一的，多用户通信和信息理论。 它的结果将影响多址技术和接收机设计的选择，以及指导渐近随机矩阵理论与技术相关问题的发展。

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.