CAJ | 학술논문

为了解决复数域下基于 QR 分解的 LLL(A. K. Lenstra, H. W. Lenstra and L. Lovász)算法中复 Givens 旋转矩形式不统一的问题,文章从复数域下原始 LLL 算法中 Gram-Schmidt 系数与 QR 分解的上三角矩阵 R 中元素之间的关系出发,证明了上三角矩阵 R 的元素与 Gram-Schmidt 系数以及 Lovász 条件之间的等价的关系;从复数的指数形式出发,推导出2种适合 LLL 算法的复 Givens 旋转矩阵形式,并证明只有其中一种符合 Lovász 条件下复Givens 旋转矩阵形式.仿真结果表明,采用基于 QR 分解的复数域 LLL 算法的 MIMO 系统相比采用基于Gram-Schmidt 正交化 LLL 算法的 MIMO 系统具有更好的误比特率性能.
위료해결복수역하기우 QR 분해적 LLL(A. K. Lenstra, H. W. Lenstra and L. Lovász)산법중복 Givens 선전구형식불통일적문제,문장종복수역하원시 LLL 산법중 Gram-Schmidt 계수여 QR 분해적상삼각구진 R 중원소지간적관계출발,증명료상삼각구진 R 적원소여 Gram-Schmidt 계수이급 Lovász 조건지간적등개적관계;종복수적지수형식출발,추도출2충괄합 LLL 산법적복 Givens 선전구진형식,병증명지유기중일충부합 Lovász 조건하복Givens 선전구진형식.방진결과표명,채용기우 QR 분해적복수역 LLL 산법적 MIMO 계통상비채용기우Gram-Schmidt 정교화 LLL 산법적 MIMO 계통구유경호적오비특솔성능.
In order to solve inconsistency of the complex Givens rotation matrix in LLL (A. K. Lenstra, H. W. Lenstra, and L. Lovász) algorithm based on the QR decomposition, from the equivalence relations between Gram-Schmidt coefficients of original LLL algorithm and elements in the upper triangular matrix R of QR decomposition, two complex Givens rotation matrices which were suitable for LLL algorithm were deduced and the Givens rotation matrix was proved meeting the Lovász conditions in terms of complex exponential expression. Simulation results showed that MIMO systems with complex field LLL algorithm based on QR decomposition had better BER (bit Error Rate) performance than the MIMO systems employing the existing complex LLL algorithm.