论文部分内容阅读
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。
In order to solve the problem of the non-uniformities of the complex Givens rotating moments in the LLL algorithm based on QR decomposition in complex domain, the paper analyzes the relationship between Gram-Schmidt coefficients and QR decomposition On the basis of the relationship between the elements in the upper triangular matrix R, the equivalence relations between the elements of the upper triangular matrix R and the Gram-Schmidt coefficient and the Lovász condition are proved. Based on the exponential form of the complex number, two suitable LLL algorithms The complex Give Give rotation matrix forms and proves that only one of them complies with Lovász condition in the form of a complex Give Give rotation matrix. The simulation results show that the MIMO system based on complex LLL algorithm based on QR decomposition has better bit error rate performance than the MIMO system based on Gram-Schmidt orthogonal LLL algorithm.