基于低空目标检测的分布式多输入多输出雷达功率分配合作博弈算法

doi:10.12382/bgxb.2023.1199

摘要/Abstract

摘要：

为提升低空突防作战场景下分布式多输入多输出(Multiple Input and Multiple Output,MIMO)雷达系统的目标检测效能,提出一种合作博弈功率分配(Cooperative Game Power Allocation,CGPA)算法。基于带误差的支援信息建立了低空多径环境下的分布式MIMO雷达信号模型,并推导了基于奈曼皮尔逊准则的检测模型。结合Max-Min准则以信干噪比(Signal to Interference plus Noise Ratio,SINR)为优化模型的效用函数。在此基础上,利用加权方法简化了联盟利益Shapley值的计算,得到满足帕累托最优性和公平性的合作资源分配方案。通过对发射功率资源的细致化管理,有效减小多径效应引起接收信号幅度的参差与衰落。在改善接收信号的稳定性的同时,挖掘并利用多径环境下丰富的散射特性,有效提升了雷达系统的探测效能。仿真实验验证了分布式MIMO雷达系统低空多径目标检测的出色性能,所提功率分配算法能够有效提升系统检测性能,并具有较好的实时性。

关键词: 分布式多输入多输出雷达系统, 目标检测, 多径效应, 功率分配, 合作博弈理论

Abstract:

To enhance the target detection efficiency of distributed multiple input and multiple output (MIMO) radar systems in low-altitude penetration combat scenarios,a cooperative game power allocation (CGPA) method is introduced.A distributed MIMO radar signal model used in a low-altitude multipath environment is established based on the support information with potential errors,and a detection model is derived based on the Neyman-Pearson criterion.The signal to interference plus noise ratio (SINR) is used as the utility function for the optimization model by incorporating the Max-Min criterion.On this basis,a weighted method is employed to streamline the computation of the Shapley value pertaining to coalition interests,therefore resulting in a cooperative resource allocation framework that meets both Pareto optimality and fairness criteria.The fluctuations and fading of received signal amplitude stemming from the multipath effect can be significantly mitigated by meticulously managing transmission power resources.Furthermore,in addition to enhancing the stability of the received signal,the abundant scattering features in the multipath environment are mined and harnessed,thereby effectively boosting the detection efficiency of the radar system.Simulated results validate the superior performance of distributed MIMO radar system for detecting the low-altitude multipath target.The proposed power allocation method significantly enhances the detection capabilities of the system while maintaining excellent real-time performance.

Key words: distributed multiple input and multiple output radar system, radar detection, multipath effect, power allocation, cooperation game theory

中图分类号:

TN957

齐铖, 谢军伟, 张浩为, 王雷, 王瑞君, 费太勇. 基于低空目标检测的分布式多输入多输出雷达功率分配合作博弈算法[J]. 兵工学报, 2025, 46(1): 231199-.

QI Cheng, XIE Junwei, ZHANG Haowei, WANG Lei, WANG Ruijun, FEI Taiyong. A Cooperative Game Power Allocation Method for Distributed MIMO Radar Detecting a Low-altitude Target[J]. Acta Armamentarii, 2025, 46(1): 231199-.

图/表 22

图1 多径几何模型

Fig.1 Multipath geometry model

图2 CGPA算法的伪代码

Fig.2 Pseudo-code for CGPA algorithm

图3 MIMO雷达低空检测性能

Fig.3 Low-altitude detection performance of distributed MIMO radar system

图4 多径影响下雷达系统信道自由度对检测性能影响

Fig.4 Impact of channel degree of freedom on the detection performance of radar system with multipath

表1 分布式MIMO雷达系统天线部署位置参数

Table 1 Antennas deployment of distributed MIMO radar system

天线	序号	x/km	y/km	z/km
发射天线	1	22.50	40.00	0.08
	2	39.82	10.00	0.08
	3	5.18	10.00	0.08
	4	39.82	30.00	0.08
	5	22.50	0	0.08
	6	5.18	30.00	0.08
接收天线	1	32.50	37.32	0.05
	2	32.50	2.68	0.05
	3	2.50	20.00	0.05
	4	42.50	20.00	0.05
	5	12.50	2.68	0.05
	6	12.50	37.32	0.05

表2 目标运动参数设置

Table 2 Target motion parameter setting

目标	初始位置/km			$v 0 q$ /(m·s^-1)	θ/rad	ϑ/rad	$A n q$ /g	$ω n q$	$φ n q$
目标	x	y	z	$v 0 q$ /(m·s^-1)	θ/rad	ϑ/rad	$A n q$ /g	$ω n q$	$φ n q$
1	0.5	0	1.0	800	0	π/4	-0.1	0.1	0
2	0	10.0	0.75	750	π/280	π/6	-0.23	0.01	0
3	45.0	25.0	0.6	750	π/240	π/8	-0.13	0.01	0

表2 目标运动参数设置

Table 2 Target motion parameter setting

目标	初始位置/km			$v 0 q$ /(m·s^-1)	θ/rad	ϑ/rad	$A n q$ /g	$ω n q$	$φ n q$
目标	x	y	z	$v 0 q$ /(m·s^-1)	θ/rad	ϑ/rad	$A n q$ /g	$ω n q$	$φ n q$
1	0.5	0	1.0	800	0	π/4	-0.1	0.1	0
2	0	10.0	0.75	750	π/280	π/6	-0.23	0.01	0
3	45.0	25.0	0.6	750	π/240	π/8	-0.13	0.01	0

表3 分布式MIMO雷达系统参数设置

Table 3 Parameter setting of distributed MIMO radar system

参数	数值	参数	数值
λ/m	0.3	ρ',ρ″	1
$σ n ~ 2$	10^-13	ε	1×10^-15
τ_c	10^-3	G_t,G_r/dB	45
I_p	100	G'_t,G'_r/dB	-20
$ξ m, n$	1	L_c,L_r/dB	15

表3 分布式MIMO雷达系统参数设置

Table 3 Parameter setting of distributed MIMO radar system

参数	数值	参数	数值
λ/m	0.3	ρ',ρ″	1
$σ n ~ 2$	10^-13	ε	1×10^-15
τ_c	10^-3	G_t,G_r/dB	45
I_p	100	G'_t,G'_r/dB	-20
$ξ m, n$	1	L_c,L_r/dB	15

图5 分布式MIMO雷达系统探测单目标场景布设

Fig.5 Deployment of distributed MIMO radar system for detecting single target

图6 单目标场景下的发射功率分配策略

Fig.6 Transmit power allocation strategy for single target scenario

图7 单目标场景下SINR比较

Fig.7 SINR comparison in a single target scenario

图8 单目标场景下两种算法的运行时间

Fig.8 Runtimes of two algorithms in the single target scenario

图9 分布式MIMO雷达系统探测多目标场景布设

Fig.9 Scenario setup of Distributed MIMO radar system detecting multi-target

图10 场景2中SINR最差目标标号

Fig.10 The index of the worst SINR target in Scenario 2

图11 多目标场景下的发射功率分配策略

Fig.11 Transmit power allocation strategy in multi-target scenario

图12 多目标场景下SINR比较

Fig.12 Comparison of SINRs in a Multi-target scenario

图13 多目标场景下两种算法的运行时间

Fig.13 Runtimes of two algorithms in the multi-target scenario

图14 雷达系统在Oxy平面上的俯瞰视图

Fig.14 Top view of C-shaped radar system on Oxy plane

图15 场景3中单目标的发射功率分配策略

Fig.15 Transmit power allocation strategy for single target in Scenario 3

图16 场景3下单目标的SINR比较

Fig.16 SINR comparison of single target in Scenario 3

图17 场景3中多目标的发射功率分配策略

Fig.17 Transmit power allocation strategy for multi-target in Scenario 3

图18 场景3多目标检测中SINR最差目标标号

Fig.18 The index of the worst SINR target in the multi-target Scenario 3

图19 场景3下多目标的SINR比较

Fig.19 SINR comparison of multi-target in Scenario 3

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