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Matrix-Monotonic Optimization for MIMO Systems

机译:MIMO系统的矩阵单调优化

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For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables, e.g., precoders, equalizers, and training sequences, are usually matrices. It is well known that matrix operations are usually more complicated compared with their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper, we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then, exploiting the framework of matrix-monotonic optimization the optimal structures of the considered matrix variables can be derived first. Based on the optimal structure, the matrix-variate optimization problems can be greatly simplified into the ones with only vector variables. In particular, the dimension of the new vector variable is equal to the minimum number of columns and rows of the original matrix variable. Finally, we also extend our work to some more general cases with multiple matrix variables.
机译:对于MIMO系统,由于在发射器和接收器处都部署了多个天线,因此设计变量(例如,预编码器,均衡器和训练序列)通常是矩阵。众所周知,矩阵运算通常比矢量运算复杂。为了克服矩阵变量导致的高复杂度,本文研究了一类优雅的多目标优化问题,即矩阵单调优化问题(MMOPs)。在我们的工作中,各种代表性的MIMO优化问题被统一到矩阵单调优化的框架中,其中包括线性收发器设计,非线性收发器设计,训练序列设计,雷达波形优化,相应的鲁棒性设计等。然后,利用矩阵单调优化的框架,可以首先得出所考虑矩阵变量的最优结构。基于最优结构,矩阵变量优化问题可以大大简化为仅具有矢量变量的问题。特别是,新向量变量的维数等于原始矩阵变量的最小列和行数。最后,我们还将工作扩展到具有多个矩阵变量的一些更一般的情况。

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