Algebraic Schemes for Space-Time Modulation in Multiple Transmit Antenna Design

为了获得这项数学科学的跨学科资助，格兰特将于2003年8月至2004年7月访问位于博尔德的科罗拉多大学的电气和计算机工程系，与他们的数字通信研究小组合作，主要目标是为具有多个发射天线的系统设计调制技术。这种调制也被称为空时编码，并且需要产生复数矩阵集，以实现最大空间分集（即，这些矩阵中的任何矩阵的差具有最大秩）。这些矩阵的条目被限制为调制方案的所谓星座点。格兰特希望建立在那些使用代数数论来构建具有最大空间分集的矩阵集的人的最近工作的基础上，这些矩阵集的条目在BPSK、QPSK和矩形QAM调制方案的星座中，该IGMS项目由MPS多学科活动办公室（OMA）联合支持，数学科学部（DMS）

For this interdisciplinary grant in the mathematical sciences, Grant will spend August 2003-July 2004 visiting the Department of Electrical and Computer Engineering at the University of Colorado atBoulder to collaborate with their research group in digital communications.The primary goal is to design modulation techniques for systems with multiple transmit antennas. This modulation is also referred to as space-time coding, and requires the production of sets of complex matriceswhich achieve maximal spatial diversity (that is, the difference of any of these matrices has maximal rank). The entries of these matrices are constrained to be so-called constellation points for the modulation scheme.Grant hopes to build upon recent work of those who have used algebraic number theory to build sets of matrices with maximal spatial diversity whose entries are in constellations for BPSK, QPSK, and rectangular QAM modulation schemes, and to apply algebraic number theory to the design ofspace-time codes for other constellations.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).