Cognitive Radio Network Downlink Power Allocation and Beamforming Method with Imperfect Channel State Information
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摘要: 针对非理想信道状态信息(CSI)条件下工作于underlay模式的认知无线网络(CRN)多用户下行功率分配和波束赋形研究中普遍存在的问题，包括忽略主网络(PN)对认知用户(SU)的干扰、传统的凸优化SDR方法对约束条件的近似要求以及实现算法复杂、实用性受限等，首先建立CRN模型，增添PN对SU的干扰项，而后在非理想CSI的最差条件下形成优化问题。再通过Lagrange对偶对问题的约束条件进行变换，并基于变换后的问题形式，利用上行和下行的对偶特性，引入虚拟功率，将优化问题转换为上行功率分配和波束赋形问题，进一步得到简便、快速和实用的迭代算法。数值仿真显示，算法收敛很快。并且发现非理想CSI引起的误差不仅对下行功率影响明显而且还改变优化问题的可行解区域；PN基站(PBS)的发送功率的变化对可行解区域有显著的影响。Abstract: Some problems of multi-user downlink power allocation and beamforming in a underlay Cognitive Radio Network (CRN) with imperfect Channel State Information (CSI) are addressed. They include ignoring the interferences of the Primary Network (PN) to the Secondary Users (SU), conventional SDR algorithm of convex optimization needing the constraint approximation, the high complexity of the algorithm, and implemented with difficulty, etc. Firstly the term of interference of the PN to the SU is added to the CRN model. The optimization problem is formulated with the worst-case imperfect CSI. Next the constraints of the problem are transformed by means of Lagrange duality. Then, based on the form of the problem, the simple, fast and practical iterative algorithm is obtained by utilizing the duality of uplink-downlink, introducing virtual power, and transforming the optimization problem into the problem of uplink power allocation and beamforming. Numerical simulation results show that it converges faster. It is also found that the errors of the imperfect CSI not only influence the downlink power but also change the feasibility region. The variation of transmitting power of the PN Base Station (PBS) could affect the feasibility region notably.
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表 1 不同收敛门限下的迭代次数
序号 1 2 3 4 5 收敛门限 $\delta $ 10–3 10–4 10–5 10–6 10–7 迭代次数 $N$ 11 17 25 47 67 
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