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Abstract

For intelligent reflection surface (IRS) assisted satellite-terrestrial integrated network (STIN), a robust secure beamforming method based on the imperfect channel state information (CSI) of eavesdroppers is proposed. First of all, considering that the satellite uses spot beam technology to serve the earth station, while the ground base station (BS) serves multiple ground users through multicast technology, and in the case of frequency spectrum shared between the two networks, a joint optimization problem is formulated to minimize the total transmit power of STIN while satisfying the quality of service constraints of the BS users and the achievable secrecy rate constraints of the earth station. Secondly, in order to solve this non-convex problem, the upper bound and the lower bound of the eavesdroppers’ output signal-to-noise ratio under the condition of imperfect CSI are derived by employing triangle inequality together with Holder inequality. Then, a joint optimization scheme of robust BF and power control based on semi-positive definite programming and penalty function method is proposed to realize the secure and reliable transmission in STIN. Finally, the simulation results verify the effectiveness and superiority of the proposed algorithm.

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Authors and contacts

Corresponding author:Lin Min,linmin@njupt.edu.cn

Funds:Project supported by the International (Regional) Cooperation and Exchange Program of the National Natural Science Foundation of China (Grant No. 61720106003) , NUPTSF (Grant Nos. NY220111, NY221009) and the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant Nos. KYCX20_0814).

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基于惩罚函数的联合优化算法流程
步骤1　初始化计算精度$\varepsilon = {10^{ - 7}}$, 惩罚因子$ \rho = 2 $和$ \mu = 2 $, 迭代次数k=0.
步骤2　使用SDR方法求解优化问题P4, 获得的初始解记为$ {{\mathbf{W}}^{(k)}} $和$ {{\mathbf{V}}^{(k)}} $.
步骤3　计算$ {{\mathbf{W}}^{(k)}} $最大特征值$ {\lambda _{\max }}\left( {{{\mathbf{W}}^{(k)}}} \right) $和对应的特征向量${\mathbf{w}}_{\max }^{(k)}$; 计算$ {{\mathbf{V}}^{(k)}} $最大特征值$ {\lambda _{\max }}\left( {{{\mathbf{V}}^{(k)}}} \right) $和对应的特征向量${\mathbf{v}}_{\max }^{(k)}$.
步骤4　求解凸优化问题P6, 获得的最优解记为$ {{\mathbf{W}}^{(k{\text{ + 1}})}} $和$ {{\mathbf{V}}^{(k{\text{ + 1}})}} $.
步骤5　如果$ {{\mathbf{W}}^{(k)}} \approx {{\mathbf{W}}^{(k{\text{ + 1}})}} $, 则更新$ \rho {\text{ = 2}}\rho $; 如果$ {{\mathbf{V}}^{(k)}} \approx {{\mathbf{V}}^{(k{\text{ + 1}})}} $, 则更新$ \mu {\text{ = 2}}\mu $;
步骤6　更新迭代次数$ k = k + 1 $.
步骤7　如果满足收敛条件$ \left\| {{\text{Tr}}\left( {{{\mathbf{W}}^{(k)}}} \right) - {\lambda _{\max }}\left( {{{\mathbf{W}}^{(k)}}} \right)} \right\| + \left\| {{\text{Tr}}\left( {{{\mathbf{V}}^{(k)}}} \right) - {\lambda _{\max }}\left( {{{\mathbf{V}}^{(k)}}} \right)} \right\| \leqslant \varepsilon $, 迭代结束, 输出W,V和P; 否则, 返回步骤3.

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Vol. 71, Issue 7 - 2022-04-05

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