CAREER: Towards Unified Theory of Wireless Communications

由于难以精确计算一些关键量，如信道容量和检测误差概率，目前大多数无线通信的分析工作都局限于一些相互分离状态下的渐近分析。因此，基于这些研究的工程结论有时是不相容的，这使得分析结果难以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，了解它们的共同影响，并将不同的理论结果综合成一个统一的图景。具体而言，本项目研究了多输入多输出（MIMO）信道和超宽带信道的新兴新技术。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，以及信道的快/慢时变。这种渐进分析大大简化了问题。然而，由于通常一个参数被孤立并取其极限，不同参数之间的关系有时会被扭曲，导致结论不一致。该项目旨在通过开发新的渐近分析方法来解决这些问题，该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、功率和能源效率、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放在一起达到它们的极限，但保持它们之间精心选择的关系。这种方法在保持渐近分析的简单性的同时，有助于描述一个连续体，该连续体弥合了不同极端情况下当前结果之间的差距。

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.