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Distributed Radar Main-lobe Interference Suppression Method Via Joint Optimization of Array Configuration and Subarray Element Number
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摘要: 针对单基雷达无法有效抑制伴随式主瓣压制干扰的问题，可通过部署稀疏辅助阵形成等效大孔径阵列，从空域上将主瓣干扰与目标进行分离，但该方法易形成空域栅瓣。针对以上问题，该文提出了一种基于阵列构型与阵元数量双参数迭代优化框架，该框架由阵列构型优化与子阵阵元数量优化两部分组成，其中阵列构型优化固定子阵阵元数量，基于最小方差无失真响应准则在主瓣干扰方向形成零陷，利用改进自适应遗传粒子群算法在孔径尺寸、子阵最小间距和主瓣干扰方向零陷深度等约束条件下优化阵列构型，抑制波束栅瓣；子阵阵元数量优化通过改进自适应遗传粒子群算法在有限子阵阵元数量、主瓣干扰方向零陷深度等约束条件下优化子阵阵元数量，进一步抑制波束栅瓣。此外，通过数值仿真验证了相同参数条件下阵列构型与阵元数量双参数迭代优化框架的有效性。最后，针对典型分布式机动平台协同探测场景，探索了主瓣干扰抑制和栅瓣抑制性能边界。
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关键词:
- 分布式雷达 /
- 主瓣干扰抑制 /
- 栅瓣抑制 /
- 双参数迭代优化框架 /
- 改进自适应遗传粒子群算法
Abstract: To address the ineffectiveness of single-base radar in suppressing adjoint main-lobe interference, an equivalent large-aperture array can be designed by deploying sparse auxiliary arrays to separate main-lobe interference from targets in the spatial domain. However, this method is prone to generating spatial grating lobes. To overcome this problem, this study proposes a dual-parameter iterative optimization framework comprising two parts: array configuration optimization and subarray element number optimization. Array configuration optimization caters to the number of subarray elements and creates nulls in the main-lobe interference direction on the basis of the minimum variance distortionless response criterion. To suppress grating lobes of the beam an improved adaptive genetic particle swarm algorithm is used to optimize the array configuration under constraints, such as aperture size, minimum subarray spacing, and null depth in the main-lobe interference direction. Subarray element number optimization uses the above-mentioned algorithm to optimize the number of subarray elements under constraints, such as a limited number of subarray elements and null depth in the main-lobe interference direction, further suppressing beam grating lobes. Finally, numerical simulations confirmed the effectiveness of the dual-parameter iterative optimization framework for array configuration and element number under the same parameter conditions. Additionally, this study explores the performance boundaries of main-lobe interference suppression and grating lobe suppression for typical distributed mobile platform cooperative detection scenarios. -
图 5 3种算法$ \gamma $与迭代次数k变化
Figure 5. $ \gamma $ versus iteration number k for three algorithms
图 6 不同P下$ \gamma $与迭代次数t关系
Figure 6. $ \gamma $ versus iteration number t for different P
图 7 不同$ {d_{\min }} $下$ \gamma $与迭代次数t关系
Figure 7. $ \gamma $ versus iteration number t for different $ {d_{\min }} $
图 8 不同$ {P_{\text{m}}} $下$ \eta $与优化次数t关系
Figure 8. $ \eta $ versus iteration number t for different $ {P_{\text{m}}} $
图 9 不同优化方式$ \eta $与迭代次数t关系
Figure 9. $ \eta $ versus iteration number t for different optimization methods
图 10 不同优化方式归一化方向图
Figure 10. Normalized beampattern for different optimization methods
图 12 主雷达回波信号脉压结果与分布式雷达回波信号处理后的脉压结果
Figure 12. Main radar echo signal pulse compression result and distributed radar echo signal processed pulse compression result
图 13 主雷达不同位置$ \eta $与迭代次数t关系
Figure 13. $ \eta $ versus iteration number t for different main radar position
图 14 方向图增益与试验次数n关系
Figure 14. Relationship between pattern gain and number of trials n
1 DPIOF算法流程
1. DPIOF algorithm flow
输入：$ {{\tilde {\boldsymbol{l}}}^{\left( 0 \right)}} $, $ {{{\boldsymbol{m}}}^{\left( 0 \right)}} $, T, P, $ {P_{\text{m}}} $, H； 输出：$ {{\tilde {\boldsymbol{l}}}_{{\text{opt}}}} $, $ {{{\boldsymbol{m}}}_{{\text{opt}}}} $, $ {\eta _{{\text{opt}}}} $； 1： $ t = 0 $； 2： $ t = t + 1 $，$ h = 0 $； 3： $ h = h + 1 $； 4： 固定$ {{\boldsymbol{m}}}_{{\text{opt}}}^{\left( {t - 1,H} \right)} $，利用IAG-PSO算法更新$ {{\tilde {\boldsymbol{l}}}^{\left( {t,h} \right)}} $，得到目标
函数值$ {\gamma ^{\left( {t,h} \right)}} $；5： 如果$ {\gamma ^{\left( {t,h} \right)}} < {\gamma ^{\left( {t - 1,H} \right)}} $，令$ {\tilde {\boldsymbol{l}}}_{{\text{opt}}}^{\left( {t,h} \right)} = {{\tilde {\boldsymbol{l}}}^{\left( {t,h} \right)}} $, $ \gamma _{{\text{opt}}}^{\left( {t,h} \right)} = {\gamma ^{\left( {t,h} \right)}} $；
否则，$ {\tilde {\boldsymbol{l}}}_{{\text{opt}}}^{\left( {t,h} \right)} = {{\tilde {\boldsymbol{l}}}^{\left( {t - 1,H} \right)}} $, $ \gamma _{{\text{opt}}}^{\left( {t,h} \right)} = {\gamma ^{\left( {t - 1,H} \right)}} $；6： 固定$ {\tilde {\boldsymbol{l}}}_{{\text{opt}}}^{\left( {t,h} \right)} $，利用IAG-PSO算法更新$ {{{\boldsymbol{m}}}^{\left( {t,h} \right)}} $，得到目标函数
值$ {\eta ^{\left( {t,h} \right)}} $；7： 如果$ {\eta ^{\left( {t,h} \right)}} < {\eta ^{\left( {t - 1,H} \right)}} $，令$ {{\boldsymbol{m}}}_{{\text{opt}}}^{\left( {t,h} \right)} = {{{\boldsymbol{m}}}^{\left( {t,h} \right)}} $, $ \eta _{{\text{opt}}}^{\left( {t,h} \right)} = {\eta ^{\left( {t,h} \right)}} $；
否则，$ {{\boldsymbol{m}}}_{{\text{opt}}}^{\left( {t,h} \right)} = {{{\boldsymbol{m}}}^{\left( {t - 1,H} \right)}} $, $ \eta _{{\text{opt}}}^{\left( {t,h} \right)} = {\eta ^{\left( {t - 1,H} \right)}} $；8： 如果$ h < H $，继续步骤3； 9： 如果$ t = T $，结束；否则，$ {\text{Initial}}\left( {{\tilde {\boldsymbol{l}}}_{{\text{opt}}}^{\left( {t,h} \right)}} \right) $，令$ {{\boldsymbol{m}}}_{{\text{opt}}}^{\left( {t,H} \right)} = {{{\boldsymbol{m}}}^{\left( 0 \right)}} $，
继续步骤2。
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2 基于IAG-PSO算法求解流程
2. IAG-PSO algorithm solution flow
输入：$ {\text{Initial}}( {{\tilde {\boldsymbol{l}}}_{{\text{opt}}}^{\left( t \right)}} ) $, P, $ {\text{NP}} $, $ {w_{\max }} $, $ {w_{\min }} $, $ {p_{\text{c}}} $, $ {p_{\text{m}}} $, K，速度和位置边界条件； 输出：$ {{\tilde {\boldsymbol{l}}}^{\left( {t + 1} \right)}} $, $ {\gamma ^{\left( {t + 1} \right)}} $； 1： $ k = 0 $，得到初始化后的新种群，计算种群中所有个体适应度$ {\gamma ^{\left( 0 \right)}}\left( j \right) $，$ j = 1,2, \cdots ,{\text{NP}} $，得到$ \gamma _{\min }^{\left( 0 \right)} $, $ \gamma _{\text{u}}^{\left( 0 \right)} $, $ {{\boldsymbol{p}}}_{{\text{best}}}^{\left( 0 \right)} $, $ {{\boldsymbol{g}}}_{{\text{best}}}^{\left( 0 \right)} $； 2： $ k = k + 1 $； 3： 计算$ c_1^{\left( k \right)} $和$ c_2^{\left( k \right)} $，计算种群中个体j权值$ w_{j}^{\left( k \right)} $，更新其速度和位置信息，越界处理，保留更新后适应度更小的个体，输出更新后种群中
个体j速度$ {{\boldsymbol{v}}}_{j}^{\left( k \right)} $和位置$ {\tilde {\boldsymbol{l}}}_{j}^{\left( k \right)} $，$ j = 1,2, \cdots ,{\text{NP}} $；4： 交叉操作，更新交叉池中个体速度$ {{\boldsymbol{v}}}_i^{\prime\left( k \right)} $和位置$ {\tilde {\boldsymbol{l}}}_i^{\prime\left( k \right)} $，越界处理，保留更新后适应度更小个体，$ i\left( {i = 1,2, \cdots ,{\text{cp}}} \right) $； 5： 变异操作，更新变异池中个体速度$ {{\boldsymbol{v}}}_i^{\prime\prime\left( k \right)} $和位置$ {\tilde {\boldsymbol{l}}}_i^{\prime\prime\left( k \right)} $，越界处理，保留更新后适应度更小个体，$ i\left( {i = 1,2, \cdots ,{\text{mp}}} \right) $； 6： 更新种群个体适应度$ {\gamma ^{\left( k \right)}}\left( j \right) $，得到$ \gamma _{\min }^{\left( k \right)} $, $ \gamma _{\text{u}}^{\left( k \right)} $, $ {{\boldsymbol{p}}}_{{\text{best}}}^{\left( k \right)} $, $ {{\boldsymbol{g}}}_{{\text{best}}}^{\left( k \right)} $； 7： 如果$ k = K $，令$ {{\tilde {\boldsymbol{l}}}^{\left( {t + 1} \right)}} = {{\boldsymbol{g}}}_{{\text{best}}}^{\left( K \right)} $, $ {\gamma ^{\left( {t + 1} \right)}} = \gamma _{\min }^{\left( K \right)} $，结束；否则，继续步骤2。
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表 1 仿真参数
Table 1. Simulation parameters
参数 数值 参数 数值 信号载频$ {f_0} $ 10 GHz 主雷达孔径 5 m 目标角度$ {\theta _0} $ 0° 信噪比SNR 20 dB 干扰角度$ {\theta _{\rm j}} $ 0.05° 干噪比INR 20 dB
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表 2 IAG-PSO算法仿真参数
Table 2. IAG-PSO algorithm simulation parameters
参数 数值 参数 数值 种群数量$ {\text{NP}} $ 100 交叉概率$ {p_{\text{c}}} $ 0.8 最大迭代次数K 30 变异概率$ {p_{\text{m}}} $ 0.3 权重最大值$ {w_{\max }} $ 1 基因数量 6 权重最小值$ {w_{\min }} $ 0.4 速度取值范围 [–2,2]
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表 3 辅助雷达阵元数量与$ {\boldsymbol{\eta}} $
Table 3. The number of auxiliary subarray elements and ${\boldsymbol{ \eta}} $
子阵 优化前 优化后 子阵2 61 61 子阵3 61 55 子阵4 61 61 子阵5 61 59 子阵6 61 47 子阵7 61 57 子阵8 61 41 $ \eta $ –6.630 dB –6.815 dB
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表 4 不同优化方式的优化结果(dB)
Table 4. Optimization results of different approaches (dB)
优化方式 $ \eta $ 优化方式1 –6.630 优化方式2 –6.355 优化方式3 –6.611 优化方式4 –0.265 DPIOF –6.815
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表 5 回波数据的仿真参数
Table 5. Simulation parameters of echo data
参数 数值 参数 数值 信号载频$ {f_0} $ 10 GHz 目标距离 9 km 信号带宽 20 MHz 采样率 50 MHz 信号脉宽 10 μs 干扰类型 噪声干扰 目标角度$ {\theta _0} $ 0° 信噪比SNR –20 dB 干扰角度$ {\theta _{\rm j}} $ 0.05° 干噪比INR 30 dB
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表 6 主雷达不同位置优化结果(dB)
Table 6. Optimization results of different positions of the main radar (dB)
主雷达位置 $ \eta $ 位置1 –6.815 位置2 –6.705 位置3 –7.790 位置4 –7.107
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