Towards a Mathematical Theory of Space-Time Codes for Multi-Antenna Wireless Communication

预计未来几代无线通信系统将为从固定到高度移动的各种用户提供各种各样的服务，如语音、视频、高速数据和交互式多媒体，其速度从行人到高速车辆，并且在广泛的室外（城市闹市区到农村）以及室内（家庭、办公楼、工厂、办公场所）。等)在日常生活中经常遇到的传播环境。手持设备或笔记本电脑的电池限制以及相对于此类服务的野心而言的带宽稀缺，决定了设计必须尽可能有效地利用这些资源的系统的必要性。该项目将重点发展基于代数数论的二维“空时”码的数学理论，以实现多天线无线通信链路上可靠、鲁棒和资源高效的数据传输。通过考虑一般编码设计标准以及与有效可解码性相关的问题，将强调性能对各种信道条件的鲁棒性。将研究可扩展的高性能空时码，该码可以动态适应由于传播环境、散射几何形状和用户移动性变化而变化的信道条件。存在和建设的问题都将被探讨。在这个项目中引入了一个新的通用性水平，以便为一个模型的代码设计获得的知识可以应用于其他模型。数学的悠久历史表明，通用性本身就可以成为好的代码应该是什么样子的指南。

AbstractIt is expected that future generations of wireless communicationsystems will provide a wide variety of services such as voice,video, high speed data, and interactive multimedia for a varietyof users ranging from the stationary to the highly mobile --- with speedsranging from the pedestrian to high vehicular speeds --- and in a widerange of outdoor (urban downtown to rural) as well as indoor(homes, office buildings, factories, etc.) propagation environmentscommonly encountered in everyday life. Battery limitations inhand-held devices or laptops and the scarcity of bandwidth relative to theambitions of such services dictate the need for designing systems in whichthese resources must be used as efficiently as possible.This project will focus on developing amathematical theory of two-dimensional ``space-time'' codes basedon algebraic number theory for reliable, robust andresource-efficient data transmission over multi-antenna wirelesscommunication links. Robustness of performance to a variety ofchannel conditions will be emphasized by considering general codedesign criteria as will problems related to efficientdecodability. Scalable, high performance space-time codes that canbe dynamically adapted to changing channel conditions due tochanges in propagation environments, scattering geometries, and usermobility will be investigated. Questions of both existenceand construction will be pursued. A new level of generality isintroduced in this project so that knowledge acquiredfor code design for one model can be applied to other models.The long history of mathematics shows that the very level ofgenerality itself can be a guide to what good codes should looklike.