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

预计未来一代的无线通信系统将为从静止到高度移动的各种用户提供各种各样的服务，例如语音、视频、高速数据和交互式多媒体-具有从行人到高速车辆的速度--以及在更大范围的室外(城市市中心到农村)以及室内(家庭、办公楼、工厂等)。日常生活中常见的传播环境。手持设备或膝上型计算机的电池限制以及与此类服务的雄心相比带宽的稀缺要求设计必须尽可能有效地利用这些资源的系统。本项目将重点发展一种基于代数理论的二维空时码的数学理论，用于在多天线无线通信链路上进行可靠、稳健和资源高效的数据传输。通过考虑一般的码设计标准以及与效率可译码相关的问题，将强调性能对各种信道条件的稳健性。可扩展的、高性能的空时码可以动态地适应由于传播环境、散射几何结构和用户移动性的变化而改变的信道条件。既有存在的问题，也有建设的问题。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。漫长的数学历史表明，通用性本身的水平可以指导好的代码应该是什么样子。

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.