Due to the difficulties in precisely computing some of the key quantities, such as the channel capacities and the detection error probabilities, most of the current analytical work in wireless communications has been limited to asymptotic analysis in a number of mutually separated regimes. As a result, the engineering conclusions based on these studies are sometimes incompatible, making it hard to apply the analytical results in the designs of practical systems. The goal of this research is to develop novel approaches to address the interactions among several key system parameters, to understand the joint impacts of them, and to synthesize the different theoretical results into one unified picture.
Specifically, this project studies the emerging new technologies in multi-input multi-output (MIMO) channels and ultra-wideband channels. Most current research on these systems has been focused on different limiting cases, including high/low signal power, wide/narrow bandwidth, and fast/slow time-variation of the channel. Such asymptotic analysis greatly simplifies the problems. However, since usually one parameter is isolated and taken to its limit, the relation among different parameters is sometimes distorted, resulting in inconsistent conclusions. This project aims to solve such problems by developing new approaches to asymptotic analysis that address the interactions among several key system parameters, including channel time-variation, power and energy efficiency, bandwidth scaling, reliability and delay requirements, and peak-to-average ratio constraints. A key component of the new approach is to take multiple parameters to their limits together, but keep a carefully chosen relation among them. Such an approach, while maintaining the simplicity of the asymptotic analysis, helps to describe a continuum that bridges the gap between the current results for different extreme cases.
