MISO系统中上下行链路对偶性分析

Duality of Uplink and Downlink Channels in MISO Systems

TDD系统中,利用上下行链路的对偶性可以将非凸的下行优化问题转换到上行链路,从而极大简化问题的分析和数值求解。上下行链路在波束成形和容量域两方面都存在对偶性。本文在统一的系统模型下,针对总功率约束和每天线功率约束两种情况,利用拉格朗日对偶法分别对波束成形对偶、容量域对偶做了推导、分析。此外,用凸优化软件包CVX简化了问题的建模。分析表明,上下行对偶等价于拉格朗日对偶,对偶问题可更一般地表示为极大极小问题。针对每天线功率约束下的波束成形问题,用迭代法和内点法分别对其进行了MATLAB仿真。仿真结果表明,非凸的下行优化问题可以利用对偶性转化为上行链路中的凸优化问题,从而得以解决。

The non-convex problems of the downlink channel can be transformed into the ones of the dual uplink channel in time division duplex（TDD） systems by uplink-downlink duality so that they are simplified and numerically traced.With Lagrangian duality,the duality on beamforming and capacity region under sum power constraint and per-antenna power constraint are deduced and analyzed,respectively.The software package convex（CVX） relevant to convex optimization is used to simplify the problem modeling.The analysis result shows that uplink-downlink duality is equivalent to Lagrangian duality.The min-max characterization is more general than uplink-downlink duality.The dual beamforming problem under per-antenna power constraint is simulated with MATLAB using the iterative algorithm and the interior point algorithm.Simulation results show that non-convex problems of the downlink channel can be resolved as a convex problem with uplink-downlink duality in the dual uplink channel.