一种基于格理论构造高维星座图的方法  

A Lattice Based Approach to the Construction of Multi-Dimensional Signal Constellations

作　　者：吴昊[1] 张建秋[1] 宋汉斌 

机构地区：[1]复旦大学信息科学与工程学院,上海200433 [2]上海无线电设备研究所,上海200090

出　　处：《电子学报》2014年第9期1672-1679,共8页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61171127)

摘　　要：星座图的增益指数是格理论中的一个术语,它可以分解成格的编码增益和星座图边界的成形增益.本文将最大化星座图增益指数的过程构造为一系列优化问题,并将星座图的几何特性作为优化问题的约束条件.由于可通过求解优化问题来得到所需的星座图,因此本文的方法可以作为一种构造高维星座图的通用方法.相比现有算法均只适用于星座点个数较少的情况,本文方法可以简便地构造星座点数目较大的高维星座图.仿真结果显示出:在星座点数目较少时,由本文方法所构造的星座图的误符号率性能与最优值十分接近;而当星座点数目较多时,本文构造的星座图较传统基于整数格的星座图具有更低的误符号率.The constellation figure of merit （CFM） ,in terms of lattice theory ,can be separated into the coding gain of a lat-tice and the shaping gain of the boundary of a constellation .In this paper ,maximizing the CFM of multi-dimensional signal constel-lations is formulated as a series of optimization problems .The geometric characteristics of signal constellations are taken as the con-straints of such problems .Since the desirable signal constellations can be achieved by solving the optimization problems ,our ap-proach can serve as a general method of the construction of multi-dimensional signal constellations .In comparison with the fact that the existing methods can only be applied when the number of signal points is small ,the proposed approach can construct large size constellations with ease .The simulation results show that the symbol error probabilities （SEP ） of small size constellations built by our approach are very close to the optimum and that the proposed large size constellations have better SEPs than the traditional con-stellations generated by integer lattices .

关 键 词：高维星座图 格 星座图增益指数 编码增益 成形增益 误符号率 

分 类 号：TN911.3[电子电信—通信与信息系统]