Random Matrices in Wireless Communication

尽管有非常强大的经济动机来接近无线信道的信息论极限，但最先进的(以第二代蜂窝无线为代表)仍然远远不能有效利用频谱和功率资源。从基本极限分析的角度来看，无线信道尤其具有挑战性。衰落、多用户干扰和无线的空间分布特性带来了相当大的困难。相关的简单规范模型和对正确的数学工具的欣赏只是最近才出现的。这项工作的重点是研究和应用大量的数学结果，这些结果在当代感兴趣的无线通信信道的分析中发挥着关键作用。在无线系统的研究中，随机矩阵是普遍存在的。例如，衰落使信道系数具有随机性和时变性，非正交码分多址系统中的扩展波形被精确地建模为随机选择，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，编码的(香农容量)和未编码的(误码率)性能(在大多数情况下)都由某些随机矩阵的特征值决定。这些矩阵往往很大，因为它们的维度随着用户数量和自由度等参数的线性增长而增长。许多信息论问题的数值模拟是有限大小矩阵的唯一替代选择，在无限大的限制下找到了优雅的确定性解。本课题系统地研究了单用户和多用户通信和信息论中出现的随机矩阵谱。它的结果将影响多址技术和接收机设计的选择，并指导渐近随机矩阵理论的发展和技术上的相关问题。

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.