Robust Resource Allocation Algorithm in MU-MISO Backscatter Communication Systems with Eavesdroppers
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摘要: 针对反向散射通信系统信道估计不准、信息容易被窃听等问题，该文提出一种基于用户窃听的多用户-多输入单输出(MU-MISO)反向散射通信系统鲁棒资源分配算法，以提高系统传输鲁棒性与信息安全性。首先，考虑基站最大功率、时间分配、信道不确定性、能量收集和保密率等约束，建立一个MU-MISO的反向散射通信系统鲁棒资源分配问题。其次，基于非线性能量收集模型和有界球形信道不确定性模型，利用变量松弛法和S过程将原NP-hard问题转化为确定性问题，随后利用连续凸近似、半正定松弛与块坐标下降法将其转化为凸优化问题求解。仿真结果表明，与传统非鲁棒算法对比，所提算法具有较高的系统容量和较低的中断概率。Abstract: Focusing on the problems of inaccurate channel estimation and easy eavesdropping of information in backscatter communication systems, a robust resource allocation algorithm for Multi-User Multi-Input Single-Output (MU-MISO) backscatter communication systems based on user eavesdropping is proposed to improve the transmission robustness and information security of the systems. Firstly, considering the constraints on the maximum power of the base station, time allocation, channel uncertainties, energy collection, and security rate, a robust resource allocation problem for MU-MISO backscatter communication systems is established. Secondly, based on the nonlinear energy harvesting model and the bounded spherical uncertainty model, the original NP-hard problem is transformed into a deterministic one by using the variable relaxation and S-Procedure methods, and then it is transformed into a convex optimization problem by using successive convex approximation, semi-positive definite relaxation and block coordinate descent methods. Simulation results show that the proposed algorithm has higher system capacity and lower outage probability compared with the traditional non-robust algorithm.
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算法1 基于块坐标下降法的鲁棒资源分配迭代算法 1. 初始化系统参数：$ K,\,M,\,{\beta _k},\,E_k^{\text{C}},\,\sigma _k^2,\,\sigma _e^2,\,T,\,\bar x_k^2,\,\bar x_k^3,\,\bar y_k^1,\,\bar \gamma _k^{\text{E}},\,\alpha _k^{\left( 0 \right)},\,{R^{{\text{sum}}(0)}} $；阈值：$r_k^{\min },\,{P^{\max }}$；估计误差上界：$\varepsilon $；收敛精度：$ \varpi $；
初始化迭代次数：$l{\text{ = }}1$。2. Repeat 3. 固定$ \alpha _k^{\left( 0 \right)} $，求解子问题1，获得$ {\boldsymbol{W}}_k^{\left( l \right) * },\,{{\boldsymbol{Z}}^{\left( l \right) * }} $。 if $ {\boldsymbol{W}}_k^{\left( l \right) * } $满足$ \text{Rank}\left({{\boldsymbol{W}}}_{k}^{\left(l\right)\ast }\right)=1 $，可以通过特征值分解获得最优波束向量，即${\boldsymbol{W}}_k^{\left( l \right) * }{\text{ = }}{\boldsymbol{w}}_k^{\left( l \right) * }{\boldsymbol{w}}_k^{\left( l \right) * {\text{H}}}$。 else if ${\boldsymbol{W}}_k^{\left( l \right) * }$的秩大于1，可以通过高斯随机化获得最优向量。 4. 固定${\boldsymbol{W}}_k^{\left( l \right) * },\,{{\boldsymbol{Z}}^{\left( l \right) * }}$，求解子问题2，获得$ \alpha _k^{\left( l \right) * } $。 5. 计算$ {R^{{\text{sum}}(l)}} $，并且更新迭代次数$l = l + 1$。 6. Until $ \left| {{R^{{\text{sum}}(l)}} - {R^{{\text{sum}}(l - 1)}}} \right| \le \varpi $。 7. Return $ {\boldsymbol{w}}_k^{{\text{opt}}}{\text{ = }}{\boldsymbol{w}}_k^{\left( l \right) * },\,{{\boldsymbol{Z}}^{{\text{opt}}}} = {{\boldsymbol{Z}}^{\left( l \right) * }},\,\alpha _k^{{\text{opt}}} = \alpha _k^{\left( l \right) * },\,{R^{{\text{sum}}}} = {R^{{\text{sum}}(l)}} $。 
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