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Element Configuration Optimization of Hybrid Distributed PA-MIMO Radar System Based on Target Detection
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摘要: 该文建立混合分布式相控阵-多输入多输出(PA-MIMO)雷达系统模型，推导出基于Neyman-Pearson (NP)准则的似然比检测(LRT)器，在收发两端实施子阵级和阵元级优化部署，达到对雷达系统中相参增益和空间分集增益协调优化的目的。针对整数规划的子阵、阵元部署模型，提出基于量子粒子群优化的随机取整(SR-QPSO)求解算法，在较少的迭代步骤内获得最优阵元配置策略，实现子阵级和阵元级之间的联合优化。最后，通过对3个典型优化问题进行数值仿真，所提出的混合分布式PA-MIMO雷达系统优化配置较其他典型雷达系统有较大提升，探测概率达到0.98，有效距离达到1166.3 km，探测性能得到显著提升。Abstract: This paper establishes a hybrid distributed Phased-Array Multiple-Input Multiple-Output (PA-MIMO) radar system model, which combines coherent processing gain and spatial diversity gain to synergistically improve the target detection performance. We derive a Likelihood Ratio Test (LRT) detector based on the Neyman-Pearson (NP) criterion for the hybrid distributed PA-MIMO radar system. The coherent processing gain and spatial diversity gain are jointly optimized by implementing subarray-level and array element–level optimal configurations at the transceiver and transmitter ends. Moreover, a Quantum Particle Swarm Optimization-based Stochastic Rounding (SR-QPSO) algorithm is proposed for the integer programming-based configuration model. This algorithm ensures that the optimal array-element configuration strategy is obtained with less iteration and achieves the joint optimization of subarray and array-element levels. Finally, simulations verify that the proposed optimal configuration offers substantial improvements compared to other typical radar systems, with a detection probability of 0.98 and an effective range of 1166.3 km, as well as a considerably improved detection performance.
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图 1 混合分布式PA-MIMO雷达结构示意图
Figure 1. Schematic diagram of the hybrid distributed PA-MIMO radar structure
图 2 混合分布式PA-MIMO雷达阵元优化配置结构图
Figure 2. Structure diagram of hybrid distributed PA-MIMO radar array element optimization configuration
图 3 混合分布式PA-MIMO雷达信号处理流程
Figure 3. Signal processing flow of hybrid distributed PA-MIMO radar
图 4 基于优化问题1的算法性能对比
Figure 4. Algorithm performance comparison based on optimization problem 1
图 5 检测概率与接收端分集自由度的关系曲线
Figure 5. Relation curves between detection probability and diversity DOF at receiver
图 6 检测概率和发射端分集自由度的关系曲线
Figure 6. Relation curves between detection probability and diversity DOF at transmitter
图 7 不同虚警概率下检测概率与接收端分集自由度的关系曲线
Figure 7. Relation curves between detection probability and diversity DOF at receiver with different false alarm probabilities
图 8 基于优化问题2的算法性能比较
Figure 8. Algorithm performance comparison based on optimization problem 2
图 9 雷达有效作用距离和接收端分集自由度的关系曲线
Figure 9. Relation curves between radar effective range and diversity DOF at receiver
图 10 雷达有效作用距离与发射端分集自由度的关系曲线
Figure 10. Relation curves between effective range of radar and diversity DOF at transmitter
图 11 不同检测概率下雷达有效作用距离与接收端分集自由度的关系曲线
Figure 11. Relation curves between radar effective range and diversity DOF at receiver with different detection probabilities
图 12 不同虚警概率下雷达有效作用距离与接收端分集自由度的关系曲线
Figure 12. Relation curves between effective range of radar and diversity DOF at receiver with different false alarm probabilities
图 13 不同检测概率下雷达阵元配置策略
Figure 13. Radar array element configuration strategies with different detection probabilities
图 14 不同虚警概率下雷达阵元配置策略
Figure 14. Radar array element configuration strategies with different false alarm probabilities
表 1 基于量子粒子群优化的随机取整求解算法流程
Table 1. SR-QPSO algorithm solution flow
(1) 初始化解空间，设定搜索维度D、种群规模W和最大迭代次
数Q，缩扩张因子$ \alpha = 0.8 $；(2) 粒子均匀随机散布于$ {\text{[}} - P_{{\text{min}}}^{},P_{{\text{max}}}^{}{\text{]}} $，记粒子位置初始值$ P_{i,t}^j $； (3) 规格化各粒子的位置参数，按照其小数位作为随机概率取整； (4) 计算个体当前位置$ {P_{i,j}}{\text{(1)}} $与全局最优位置$ {P_{\text{g}}}{\text{(}}t{\text{)}} $； (5) 设定收缩因子的上下界${\alpha _0}$和${\alpha _1}$； (6) 计算量子行为粒子的吸引子$ p_{i,j}^{}{\text{(}}t{\text{)}} $； (7) for $ t = 1 $ to Q do (8) 计算t 时刻迭代时的平均最好个体位置； (9) for $ i = 1 $ to W do (10) 计算粒子并更新粒子位置$ P_{i,j}^{}{\text{(}}t{\text{)}} $，按照其小数
位作为随机概率取整；(11) 若$ P_{i,j}^{}{\text{(}}t{\text{)}} \notin {\text{[}} - P_{{\text{min}}}^{},P_{{\text{max}}}^{}{\text{]}} $，设置$ P_{i,j}^{}{\text{(}}t + 1{\text{)}} $
为最近的边界值；(12) end for (13) end for 
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表 2 各算法计算复杂度对比
Table 2. Algorithm computational complexity comparison
算法 计算复杂度 SR-QPSO ${\mathcal{O} }(QW)$ SR-PSO ${\mathcal{O} }(QW)$ 穷举搜索法 $ > {\mathcal{O}}({2^{M + N}}) $
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表 3 优化效果分析
Table 3. Optimization effect analysis
项目 最优指标值 配置策略 收敛时间 优化问题1 $ {P_{{\text{D}}\max }} = 0.98 $ $ {\text{(}}\hat M,\hat N{\text{)}} = {\text{(}}1,13{\text{)}} $ 87.275 s 优化问题2 ${R_{{\rm{E}}\max } } = 1166.3\;{\text{km} }$ $ {\text{(}}\hat M,\hat N{\text{)}} = {\text{(}}1,5{\text{)}} $ 86.778 s 优化问题3 $ M,\hat M $ 取决于$ {P_{{\text{FA}}}} $, $ {P_{\text{D}}} $ / MIMO雷达 ${P_{\text{D} } } = 0.63,\;{R_{\rm{E}}} = 1006\;{\text{km} }$ $ {\text{(}}\hat M,\hat N{\text{)}} = {\text{(}}100,100{\text{)}} $ / 相控阵雷达 ${P_{\text{D} } } = 0.80,\;{R_{\rm{E}}} = 1000\;{\text{km} }$ $ {\text{(}}\hat M,\hat N{\text{)}} = {\text{(}}1,1{\text{)}} $ /
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