有限字符约束下的MIMO信道线性预编码设计

Linear precoding design for MIMO channels with finite alphabet constraints

考虑到实际通信系统中的信道输入是有限字符输入,研究了有限字符输入约束下的预编码矩阵的设计和优化问题,而且以最大化多输入多输出(MIMO)系统的互信息量为目标函数,提出了一种有限字符约束情况下的预编码矩阵设计方案。该方案将预编码矩阵优化问题转化为功率分配矩阵设计和右预编码矩阵设计两个子问题。对于功率分配问题,考虑到是一个凸优化问题,利用经典的最陡下降算法进行迭代优化;对于右奇异值优化问题,考虑到是一个具有酉矩阵约束的优化问题,将该问题转化为黎曼几何上的无约束的优化问题,通过酉矩阵的李群上的最陡下降算法进行求解。试验结果表明,提出的预编码设计方案具有很好的性能,而且收敛速度较快。

Considering that the channel input of a practical communication system is finitealphabetic, the design and op timization of precoding matrixes were studied under the finite alphabet input, and a scheme for precoding metrix de sign was proposed by taking the maximized mutual information of a multiple input and multiple output （MIMO） sys tem as an objective function. The scheme translates the problem of precoding matrix design into two sub problems of designing the power allocation matrix and the right unitary matrix. The first problem is a convex optimization prob lem and it can be solved by the classical steepest descent algorithm. The second problem is a unitarymatrix con strained optimization problem, and it can be translated into a problem without constraints in the Riemannian geome try. Consequently, it can be solved by the steepest descent （SD） algorithms on the Lie group of unitary matrices. The simulation results show that the proposed algorithm has the good performance and the high speed in convergences.