CAREER: Towards Unified Theory of Wireless Communications

由于在精确计算一些关键量，如信道容量和检测错误概率的困难，大多数目前的分析工作，在无线通信已被限制在一些相互分离的制度的渐近分析。因此，基于这些研究的工程结论有时是不相容的，使得难以将分析结果应用于实际系统的设计。本研究的目标是开发新的方法来解决几个关键系统参数之间的相互作用，了解它们的联合影响，并将不同的理论结果综合成一个统一的图片，具体来说，本项目研究多输入多输出（MIMO）信道和超宽带信道中出现的新技术。目前对这些系统的研究主要集中在不同的限制情况下，包括高/低信号功率，宽/窄带宽，快/慢的信道时变。 这种渐近分析大大简化了问题。然而，由于通常一个参数是孤立的，并采取其极限，不同的参数之间的关系有时会被扭曲，导致不一致的结论。本项目旨在通过开发新的渐近分析方法来解决这些问题，这些方法解决了几个关键系统参数之间的相互作用，包括信道时变、功率和能量效率、带宽缩放、可靠性和延迟要求以及峰均比约束。新方法的一个关键组成部分是将多个参数一起带到它们的极限，但在它们之间保持精心选择的关系。这种方法，同时保持了渐近分析的简单性，有助于描述一个连续的桥梁之间的差距差距目前的结果为不同的极值情况。

Due to the difficulties in precisely computing some of the keyquantities, such as the channel capacities and the detection errorprobabilities, most of the current analytical work in wirelesscommunications has been limited to asymptotic analysis in a number ofmutually separated regimes. As a result, the engineering conclusionsbased on these studies are sometimes incompatible, making it hard toapply the analytical results in the designs of practical systems. Thegoal of this research is to develop novel approaches to address theinteractions among several key system parameters, to understand thejoint impacts of them, and to synthesize the different theoreticalresults into one unified picture.Specifically, this project studies the emerging new technologies inmulti-input multi-output (MIMO) channels and ultra-widebandchannels. Most current research on these systems has been focused ondifferent limiting cases, including high/low signal power, wide/narrowbandwidth, and fast/slow time-variation of the channel. Suchasymptotic analysis greatly simplifies the problems. However, sinceusually one parameter is isolated and taken to its limit, the relationamong different parameters is sometimes distorted, resulting ininconsistent conclusions. This project aims to solve such problems bydeveloping new approaches to asymptotic analysis that address theinteractions among several key system parameters, including channeltime-variation, power and energy efficiency, bandwidth scaling,reliability and delay requirements, and peak-to-average ratioconstraints. A key component of the new approach is to take multipleparameters to their limits together, but keep a carefully chosenrelation among them. Such an approach, while maintaining thesimplicity of the asymptotic analysis, helps to describe a continuumthat bridges the gap between the current results for different extremecases.