CAREER: Towards Unified Theory of Wireless Communications

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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.