CAJ | 학술논문

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。
성좌도적증익지수시격이론중적일개술어，타가이분해성격적편마증익화성좌도변계적성형증익。본문장최대화성좌도증익지수적과정구조위일계렬우화문제，병장성좌도적궤하특성작위우화문제적약속조건。유우가통과구해우화문제래득도소수적성좌도，인차본문적방법가이작위일충구조고유성좌도적통용방법。상비현유산법균지괄용우성좌점개수교소적정황，본문방법가이간편지구조성좌점수목교대적고유성좌도。방진결과현시출：재성좌점수목교소시，유본문방법소구조적성좌도적오부호솔성능여최우치십분접근；이당성좌점수목교다시，본문구조적성좌도교전통기우정수격적성좌도구유경저적오부호솔。
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 .