Spatial Deployment and Beamforming for Design Multi-Unmanned Aerial Vehicle-Integrated Sensing and Communication Based on Transmission Fairness
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摘要: 针对农村偏远地区通信不畅的临时突发性问题，该文提出一种自适应的多无人机(UAV)辅助通感一体化(ISAC)机制，在地面用户和感测目标呈簇状随机分布的情况下，通过合理调度多无人机实现覆盖式通信保障，为无人机使能的通感一体系统提供了一种新的解决思路和方案。该文主要研究了无人机空间部署及其对地面设备的波束成形等问题，在空地关联约束条件下，系统可通过优化无人机的通信和感知波束成形变量组，最大限度地提高用户传输可达速率的下限，同时保证基本的通感需求。为了有效解决所考虑的非凸优化问题，该文借助基于高斯核的均值漂移算法(MS)，用以处理关联策略中的混合整型线性问题，此外，结合2次变换与连续凸逼近(SCA)的相关技巧，采用块坐标下降(BCD)的方式优化波束成形，以获取次优解。数值结果验证了自适应机制的有效性。Abstract: In response to the temporary and emergent issue of poor communication in rural and remote areas, an adaptive multi-Unmanned Aerial Vehicle (UAV)-assisted Integrated Sensing And Communication (ISAC) mechanism is proposed in this paper. In scenarios where ground users and sensing targets are randomly distributed in clusters, the mechanism achieves comprehensive communication coverage by rationally scheduling multiple UAVs, providing a novel solution and scheme for UAV-enabled ISAC systems. The spatial deployment of UAVs and their beamforming directed towards ground equipment are primarily addressed in this paper. Under the constraints of the air-ground association policy, the system can maximize the lower bound of the users’ transmission reachable rate by optimizing the set of communication and sensing beamforming variables for the UAVs, while ensuring the basic requirements of ISAC. To solve the considered non-convex optimization problems, the Mean Shift (MS) algorithm based on Gaussian kernels to manage the mixed-integer linear issues within the association strategy is first employed. Additionally, combining the quadratic transformation and Successive Convex Approximation (SCA), the optimization of beamforming is conducted via the Block Coordinate Descent (BCD) method, thereby securing a suboptimal solution. Numerical results validate the effectiveness of the adaptive mechanism.
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1 空地关联与空中基站二维笛卡尔坐标部署的解决策略
步骤1 初始化地面用户(目标)集合，设定初始迭代次数为${l_1} = 1$，任选一用户或目标点作为中心点，位置为$ {\boldsymbol{q}}_i^1,i \in \{ 1,2,\cdots,K + J\} $； 步骤2 计算均值漂移向量${\boldsymbol{M}}\left( {{\boldsymbol{q}}_i^{{l_1}}} \right)$，其中半径$r$设为${d_{{\text{min}}}}$，注意：同一水平面无人机满足防撞约束，则3维环境下同样适用； 步骤3 移动密度估计窗口${\boldsymbol{q}}_i^{{l_1} + 1} = {\boldsymbol{q}}_i^{{l_1}} + {\boldsymbol{M}}\left( {{\boldsymbol{q}}_i^{{l_1}}} \right)$； 步骤4 迭代更新${l_1} = {l_1} + 1$； 步骤5 当均值漂移向量的模值小于阈值$ \varepsilon _{{\mathrm{th}}}^{\boldsymbol{q}} $或移动窗口内用户(目标)数不再增加时，迭代停止，否则重复步骤2～4； 步骤6 重新选定未被覆盖的随机点作为中心点，继续执行步骤2～5，直至所有用户(目标)点都被分配到对应聚类中心； 步骤7 构建Voronoi图和相应的凸包区域； 步骤8 计算凸包区域范围内的所有用户(目标)的位置均值； 步骤9 输出所有聚类中心坐标和对应坐标下的聚类用户(目标)。 
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2 无人机通信波束成形子算法
步骤1 初始化通信波束成形${\boldsymbol{W}}_{b,k}^{\left( 0 \right)}$，设定初始迭代次数为
${l_2} = 1$, $b = 1$；步骤2 给定${\boldsymbol{W}}_{b,k}^{\left( {{l_2} - 1} \right)}$，利用式 (18) 更新辅助变量$\delta _{b,k}^{\left( {{l_2}} \right)}$； 步骤3 给定${\boldsymbol{W}}_{b,k}^{\left( {{l_2} - 1} \right)}$和$\delta _{b,k}^{\left( {{l_2}} \right)}$，求解问题P3.1.1，获得${\boldsymbol{W}}_{b,k}^{\left( {{l_2}} \right)}$，
迭代更新${l_2} = {l_2} + 1$；步骤4 当信息传输速率增量小于阈值$\varepsilon _{{\text{th}}}^{\boldsymbol{V}}$时，迭代停止，否则重
复步骤2～3；步骤5 无人机选择切换$b = b + 1$，继续执行步骤2～4，直至所
有无人机的通信波束成形均已优化；步骤6 输出所有无人机通信波束成形矩阵${{\boldsymbol{W}}_{b,k}}$。
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3 无人机感知波束成形子算法
步骤1 初始化感知波束成形${\boldsymbol{V}}_{b,j}^{\left( 0 \right)}$，设定初始迭代次数为${l_3} = 1$,$b = 1$； 步骤2 给定${\boldsymbol{V}}_{b,j}^{\left( {{l_3} - 1} \right)}$，求解凸优化问题P3.2.1，获取${\boldsymbol{V}}_{b,j}^*$，令${\boldsymbol{V}}_{b,j}^{\left( {{l_3}} \right)} = {\boldsymbol{V}}_{b,j}^*$，迭代更新${l_3} = {l_3} + 1$； 步骤3 当信息传输速率增量小于阈值$\varepsilon _{{\text{th}}}^{\boldsymbol{V}}$时，迭代停止，否则重复步骤2； 步骤4 无人机选择切换$b = b + 1$，继续执行步骤2～3，直至所有无人机的感知波束成形均已优化； 步骤5 输出所有无人机感知波束成形矩阵$ {{\boldsymbol{V}}_{b,j}} $。
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4 无人机波束成形总体算法
步骤1 初始化通信和感知波束成形${\boldsymbol{W}}_{b,k}^{\left( 0 \right)}$, ${\boldsymbol{V}}_{b,j}^{\left( 0 \right)}$，设定初始迭
代次数为${l_4} = 1$, $b = 1$；步骤2 给定${\boldsymbol{W}}_{b,k}^{\left( {{l_4} - 1} \right)}$,${\boldsymbol{V}}_{b,j}^{\left( {{l_4} - 1} \right)}$，通过算法2求解通信波束成形子
问题，获得${\boldsymbol{W}}_{b,k}^{\left( {{l_4}} \right)}$；步骤3 给定${\boldsymbol{W}}_{b,k}^{\left( {{l_4}} \right)}$,${\boldsymbol{V}}_{b,j}^{\left( {{l_4} - 1} \right)}$，通过算法3求解感知波束成形子
问题，获得${\boldsymbol{V}}_{b,j}^{\left( {{l_4}} \right)}$；步骤4 迭代更新${l_4} = {l_4} + 1$，当信息传输速率增量小于阈值
$\varepsilon _{{\mathrm{th}}}^{{\mathrm{all}}}$时，迭代停止，否则重复步骤2～3；步骤5 无人机选择切换$b = b + 1$，继续执行步骤2～4，直至所
有无人机的波束成形均已优化；步骤6 输出所有无人机波束成形矩阵${{\boldsymbol{W}}_{b,k}}$, $ {{\boldsymbol{V}}_{b,j}} $。
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表 1 主要仿真参数
参数名称 数值 单位距离的信道功率增益${\beta _0}$ –60 dB 噪声功率${\sigma ^2}$ –110 dBm 无人机防撞距离${d_{{\text{min}}}}$ 0.3 km 单无人机发射功率上限${P_{{\text{max}}}}$ 0.5 W 波束图增益下限${\Gamma _{{\text{th}}}}$ –17 dBm 迭代收敛阈值$ \varepsilon _{{\text{th}}}^{\boldsymbol{q}},\varepsilon _{{\text{th}}}^{\boldsymbol{W}},\varepsilon _{{\text{th}}}^{\boldsymbol{V}},\varepsilon _{{\text{th}}}^{{\text{all}}} $ $1 \times {10^{ - 4}}$
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