This paper considers linear transceiver design for amplify-and-forward multiple-input multiple-output (MMO) multiple-relay systems,aiming to minimize the mean squared error (MSE) under the total relay transmit power constraint.We first introduce the singular value decomposition (SVD) of matrix product and simplify the original optimization problem to one which takes a singular value vector and a unitary matrix as optimization variables.By employing variable substitution and penalty term, the simplified problem only has one unitary matrix constraint.Then we develop a new Riemann Euclidean steepest descent algorithm to deal with the unitary matrix constraint.Finally,simulation results demonstrate that the performance of the proposed scheme is better than traditional schemes and closes to the lower bound of MSE.%本文以放大转发MIMO多中继系统为研究对象,研究其联合线性收发机的优化设计问题,其基本思想是在中继的总发射功率约束下,最小化系统的均方误差(MSE).为降低系统复杂度,本文首先引入了乘积矩阵的奇异值分解,把收发机的设计简化为以奇异值向量和酉矩阵为优化变量的优化问题;接着利用变量替换并引入罚项,将简化后的问题转化成只有酉矩阵约束的优化问题.在此基础上,通过引入替换变量的欧氏梯度,设计了新的黎曼欧氏最陡下降算法,从而有效地处理酉矩阵约束.仿真结果表明,与传统的设计方法相比,本文提出的方案性能最优,最接近MSE下界.
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