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摘要: 针对传统分布式雷达网络(DRN)数据回传成本高、效率低的问题，该文研究了一种面向空中计算(AirComp)辅助的分布式雷达网络新架构，旨在提升协同目标检测性能与数据融合效率。首先，从感知层面推导了适用于分布式雷达网络的协同检测器，创新性地揭示了其检测统计量天然具有求和形式，与AirComp的线性叠加机制在数学上高度契合。基于此，该文将各雷达节点的局部对数似然比作为AirComp的聚合对象，使AirComp的计算MSE直接对应检测充分统计量的估计误差，从而建立AirComp精度与检测性能之间的理论关联。并进一步提出一种面向AirComp辅助分布式雷达网络的联合波束赋形设计方法，同步优化雷达发射波束赋形矩阵、接收滤波器以及融合中心(FC)的混合波束赋形(HBF)接收器，并设计了基于交替优化的高效求解算法。仿真结果表明，在相同信干噪比和虚警概率条件下，所提AirDRN架构相较于传统时分双工(TDD)模式具有更优的目标检测性能，在信干噪比分别为7 dB和10 dB时，检测性能分别提升约3.17倍和1.52倍。Abstract: Aiming at the problems of high data backhaul cost and low efficiency in the traditional Distributed Radar Network (DRN), this paper investigates a novel architecture of distributed radar networks assisted by Over-the-Air Computation (AirComp), so as to improve the performance of cooperative target detection and the efficiency of data fusion. Firstly, a cooperative detector applicable to distributed radar networks is derived at the sensing level, which reveals that its detection statistic inherently takes a summation form and is highly mathematically consistent with the linear superposition mechanism of AirComp. On the basis of this inherent correlation, a joint beamforming design method is proposed for AirComp-assisted distributed radar networks, which simultaneously optimizes the radar transmit beamforming matrix, the receive filter, and the Hybrid Beamforming (HBF) receiver at the Fusion Center (FC). Furthermore, an efficient solution algorithm based on alternating optimization is devised. Simulation results demonstrate that, under the same Signal to Interference-plus-Noise Ratio (SINR) and false alarm probability, the proposed AirComp-aided Distributed Radar Network (AirDRN) architecture achieves superior target detection performance compared with the conventional Time Division Duplex (TDD) mode. Specifically, when the SINR is 7 dB and 10 dB, respectively, the detection performance is improved by approximately 3.17 and 1.52 times.
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图 1 基于空中计算的分布式雷达网络场景图
Figure 1. Scenario of the over-the-air computation-based distributed radar network
图 3 所提AirDRN-HBF算法的收敛性能
Figure 3. Convergence performance of the proposed AirDRN-HBF algorithm
图 4 不同参数下的收敛曲线对比
Figure 4. Comparison of convergence curves under different parameter settings
图 5 不同参数下接收方向图对比
Figure 5. Comparison of receive beampatterns under different parameter settings
图 6 不同工作模式下的检测概率对比
Figure 6. Comparison of detection performance under different operating modes
1 AirDRN-HBF算法
1. AirDRN-HBF algorithm
1. 输入：系统参数。 2. 当算法未收敛时，执行以下循环： 3. 通过求解式(34)更新数字接收滤波矩阵$ {\left\{{\boldsymbol{w}}_{m}\right\}}^{t+1} $。 4. 通过求解式(36)更新矩阵$ {\left\{{\boldsymbol{G}}_{m}\right\}}^{t+1} $。 5. 通过求解式(38)更新矩阵$ {\left\{\boldsymbol{Y}\right\}}^{t+1} $。 6. 通过求解问题(42)更新矩阵$ {\left\{{\boldsymbol{U}}_{m}\right\}}^{t+1} $。 7. 通过求解式(46)更新$ {\left\{{\boldsymbol{V}}_{\text{bb}}\right\}}^{t+1} $。 8. 设置初始参数：$ {\left\{\boldsymbol{Y}\right\}}^{t+1} $, $ {\boldsymbol{D}}^{t} $；初始化：$ \boldsymbol{V}_{\text{rf}}^{}\in {\mathcal{M}}_{c} $,
$ {\text{grad}}^{+}f\left(\boldsymbol{V}_{\text{rf}}^{\left(0\right)}\right)=-\text{grad}f\left(\boldsymbol{V}_{\text{rf}}^{\left(0\right)}\right) $。9. 当算法未收敛时，执行以下循环： 10. 通过Armijo准则确定$ {\kappa }^{\left(q\right)} $。 11. 通过式(55)更新$ \boldsymbol{V}_{\text{rf}}^{\left(q+1\right)} $。 12. 通过式(53)更新$ {\tau }^{\left(q+1\right)} $。 13. 通过式(52)更新$ {\text{grad}}^{+}f\left(\boldsymbol{V}_{\text{rf}}^{\left(q+1\right)}\right) $。 14. 结束循环 输出：$ {\left\{{\boldsymbol{V}}_{\text{rf}}\right\}}^{t+1}=\boldsymbol{V}_{\text{rf}}^{q+1} $ 15. 计算中间变量$ {\boldsymbol{D}}^{t+1} $和$ {\boldsymbol{Z}}^{t+1} $ 16. 结束循环 17. 收敛后，将最终迭代结果赋值为输出变量： $ {\left\{{\boldsymbol{w}}_{m}\right\}}^{l}={\left\{{\boldsymbol{w}}_{m}\right\}}^{t+1} $,$ {\left\{{\boldsymbol{U}}_{m}\right\}}^{l}={\left\{{\boldsymbol{U}}_{m}\right\}}^{t+1} $, $ \boldsymbol{V}_{\text{bb}}^{l}=\boldsymbol{V}_{\text{bb}}^{t+1} $,
$ \boldsymbol{V}_{\text{rf}}^{l}=\boldsymbol{V}_{\text{rf}}^{t+1} $18. 输出：$ {\left\{{\boldsymbol{w}}_{m}\right\}}^{l} $, $ {\left\{{\boldsymbol{U}}_{m}\right\}}^{l} $, $ \boldsymbol{V}_{\text{bb}}^{l} $, $ \boldsymbol{V}_{\text{rf}}^{l} $ 
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