A Cooperative Game Power Allocation Method for Distributed MIMO Radar Detecting a Low-altitude Target

doi:10.12382/bgxb.2023.1199

Abstract

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

CLC Number:

TN957

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-.

Figures/Tables 22

Fig.1 Multipath geometry model

Fig.2 Pseudo-code for CGPA algorithm

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

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

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

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

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

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

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

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

Fig.6 Transmit power allocation strategy for single target scenario

Fig.7 SINR comparison in a single target scenario

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

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

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

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

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

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

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

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

Fig.16 SINR comparison of single target in Scenario 3

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

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

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

References 47

[1]	杜鑫, 刘巍, 孙应飞. 针对低空目标的分布式组网探测[J]. 系统工程与电子技术, 2020, 42(5):1057-1062. doi: 10.3969/j.issn.1001-506X.2020.05.12
	DU X, LIU W, SUN Y F. Distributed network detection for low-altitude targets[J]. Systems Engineering and Electronics, 2020, 42(5):1057-1062. (in Chinese) doi: 10.3969/j.issn.1001-506X.2020.05.12
[2]	CHEN H W, TA S Y, SUN B. Cooperative game approach to power allocation for target tracking in distributed MIMO radar sensor networks[J]. IEEE Sensors Journal, 2015, 15(10):5423-5432.
[3]	SEN S, NEHORAI A. Adaptive OFDM radar for target detection in multipath scenarios[J]. IEEE Transactions on Signal Processing, 2011, 59(1):78-90.
[4]	JANG Y, LIM H, YOON D. Multipath effect on radar detection of nonfluctuating targets[J]. IEEE Transactions Aerospace and Electronic Systems, 2015, 51(1):792-795.
[5]	ZHANG H W, LIU W J, FEI T Y, et al. An efficient radar-target assignment and power allocation strategy for low-angle tracking in the MIMO-multisite radar system[J]. Signal Processing, 2022,200:108645.
[6]	YAN J K, PU W Q, LIU H W, et al. Robust chance constrained power allocation scheme for multiple target localization in colocated MIMO radar system[J]. IEEE Transactions on Signal Processing, 2018, 66(15):3946-3957.
[7]	LI J, STOICA P. MIMO radar with colocated antennas[J]. IEEE Signal Processing Magazine, 2007, 24(5):106-114.
[8]	HAIMOVICH A M, BLUM R S, CIMINI L J. MIMO Radar with widely separated antennas[J]. IEEE Signal Processing Magazine, 2007, 25(1):116-129.
[9]	DING J C, CHEN H W, WANG H Q, et al. Non-fluctuating target detection in low-grazing angle with MIMO radar[J]. Journal of Central South University, 2013, 20(10):2728-2734.
[10]	FISHLER E, HAIMOVICH A, BLUM R S, et al. Spatial diversity in radars-models and detection performance[J]. IEEE Transactions on Signal Processing, 2006, 54(3):823-838.
[11]	LIAN H, YANG M L, ZHANG Z M, et al. Multistatic radar target detection based on the time reversal in clutter environments[J]. Signal Processing, 2023,203:108789.
[12]	FANTE R L, TORRES J A. Cancellation of diffuse jammer multipath by an airborne adaptive radar[J]. IEEE Transactions Aerospace and Electronic Systems, 1995, 31(2):805-820.
[13]	JIN Y W, MOURA J M F, O’DONOUGHUE N. Time reversal in multiple-input multiple-output radar[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(1):210-225.
[14]	O’DONOUGHUE N, MOURA J M F. Gaussian target detection in multipath clutter with single-antenna time reversal[J]. IEEE Transactions on Signal Processing, 2013, 61(15):3733-3744.
[15]	SHI J P, HU G P, ZHOU H. Entropy-based multipath detection model for MIMO radar[J]. Journal of Systems Engineering and Electronics, 2017, 28(1):51-57. doi: 10.21629/JSEE.2017.01.07
[16]	ZHENG Z X, ZHANG Y, PENG X Y, et al. MIMO radar waveform design for multipath exploitation using deep learning[J]. Remote Sensing, 2023, 15(11):2747.
[17]	XU Z, FAN C Y, HUANG X T. MIMO radar waveform design for multipath exploitation[J]. IEEE Transactions on Signal Processing, 2021,69:5359-5371.
[18]	GODRICH H, PETROPULU A P, POOR H V. Power allocation strategies for target localization in distributed multiple-radar architectures[J]. IEEE Transactions on Signal Processing, 2011, 59(7):3226-3240.
[19]	SHI C G, WANG Y J, SALOUS S, et al. Joint transmit resource management and waveform selection strategy for target tracking in distributed phased array radar network[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 58(4):2762-2778.
[20]	SHI C, DING L, WANG F, et al. Joint target assignment and resource optimization framework for multitarget tracking in phased array radar network[J]. IEEE Systems Journal, 2021, 15(3):4379-4390.
[21]	YAN J K, JIAO H, PU W Q, et al. Radar sensor network resource allocation for fused target tracking:a brief review[J]. Information Fusion, 2022,86-87:104-115.
[22]	李正杰, 陈红印, 谢军伟, 等. 一种防空服务质量模型下的集中式多输入多输出雷达三维机动跟踪功率分配方法[J]. 兵工学报, 2024, 45(4):1321-1331. doi: 10.12382/bgxb.2022.1252
	LI Z J, CHEN H Y, XIE J W, et al. A power allocation method for three-dimensional maneuvering tracking in colocated MIMO radar under air defense QoS model[J]. Acta Armamentarii, 2024, 45(4):1321-1331. (in Chinese)
[23]	SHI C U, DAI X R, WANG Y J, et al. Joint route optimization and multidimensional resource management scheme for airborne radar network in target tracking application[J]. IEEE Systems Journal, 2022, 16(4):6669-6680.
[24]	WANG Y D, LIANG Y, ZHANG H X, et al. Domain knowledge-assisted deep reinforcement learning power allocation for MIMO radar detection[J]. IEEE Sensors Journal, 2022, 22(23):23117-23128.
[25]	ABAPOUR S, NAZARI-HERIS M, MOHAMMADI-IVATLOO B, et al. Game theory approaches for the solution of power system problems:a comprehensive review[J]. Archives of Computational Methods in Engineering, 2020, 27(1):81-103.
[26]	SHI C G, QIU W, WANG F, et al. Power control scheme for spectral coexisting multistatic radar and massive MIMO communication systems under uncertainties:a robust Stackelberg game model[J]. Digital Signal Processing, 2019,94:146-155.
[27]	SHI C G, DING L T, WANG F, et al. Cooperative LPI performance optimization for multistatic radar under uncertainties:a robust Stackelberg game perspective[C]//Proceedings of the 2020 IEEE 11st Sensor Array and Multichannel Signal Processing Workshop.Hangzhou, China:IEEE, 2020.
[28]	HE B, SU H T, HUANG J S. Joint beamforming and power allocation between a multistatic MIMO radar network and multiple targets using game theoretic analysis[J]. Digital Signal Processing, 2021,115:103085.
[29]	JIN B, KUANG X F, LIU S J, et al. Joint allocation of transmit power and signal bandwidth for distributed cognitive tracking radar network using cooperative game[J]. Digital Signal Processing, 2023,135:103964.
[30]	GHAREHSHIRAN O N, KRISHNAMURTHY V. Coalition formation for bearings-only localization in sensor networks-a cooperative game approach[J]. IEEE Transactions on Signal Processing, 2010, 58(8):4322-4338.
[31]	GODRICH H, HAIMOVICH A M, BLUM R S. Target localization accuracy gain in MIMO radar-based systems[J]. IEEE Transactions on Information Theory, 2010, 56(6):2783-2803.
[32]	WANG Y L, WU Y, SHEN Y. Joint spatiotemporal multipath mitigation in large-scale array localization[J]. IEEE Transactions on Signal Processing, 2019, 67(3):783-797.
[33]	汪安戈, 胡国平, 周豪. 雷达多径效应抑制技术分析及展望[J]. 火力与指挥控制, 2019, 44(5):12-21.
	WANG A G, HU G P, ZHOU H. Analysis and prospect of radar multipath effect mitigation technology[J]. Fire Control & Command Control, 2019, 44(5):12-21. (in Chinese)
[34]	FISHLER E, HAIMOVICH A, BLUM R S, et al. Spatial diversity in radars—Models and detection performance[J]. IEEE Transactions on Signal Processing, 2006, 54(3):823-838.
[35]	ZHOU H, HU G P, SHI J P, et al. Weighted target detector via estimated SNR in a multipath environment[J]. The Journal of Engineering, 2019, 2019(20):7119-7124.
[36]	周生华, 刘宏伟, 刘保昌, 等. 信噪比加权空间分集雷达目标检测算法[J]. 西安电子科技大学学报, 2011, 38(4):82-88.
	ZHOU S H, LIU H W, LIU B C, et al. Signal-to-noise Ratio weighted spatial diversity radar target detection algorithm[J]. Journal of Xidian University, 2011, 38(4):82-88. (in Chinese)
[37]	XU J, DAI X Z, XIA X G, et al. Optimizations of multisite radar system with mimo radars for target detection[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(4):2329-2343.
[38]	RICHARDS M A. Fundamentals of radar signal processing[M]. 2nd edition.Columbus,OH, US:McGraw-Hill, 2005.
[39]	YAN J K, LIU H W, JIU B, et al. Simultaneous multibeam resource allocation scheme for multiple target tracking[J]. IEEE Transactions on Signal Processing, 2015, 63(12):3110-3122.
[40]	YAN J K, LIU H W, PU W Q, et al. Joint beam selection and power allocation for multiple target tracking in netted colocated MIMO radar system[J]. IEEE Transactions on Signal Processing, 2016, 64(24):6417-6427.
[41]	ZHANG H W, LIU W J, ZONG B F, et al. An efficient power allocation strategy for maneuvering target tracking in cognitive MIMO radar[J]. IEEE Transactions on Signal Processing, 2021,69:1591-1602.
[42]	AMARIS H, MOLINA Y P, ALONSO M, et al. Loss allocation in distribution networks based on aumann-shapley[J]. IEEE Transaction on Power System, 2018, 33(6):6655-6666.
[43]	SHAPLEY L S. Cores of convex games[J]. International Journal of Game Theory, 1971, 1(1):11-26.
[44]	MYERSON R B. Graphs and cooperation in games[M] //DUTTAB, JACKSONM O. Networks and Groups: Models of strategic formation. Berlin,Heidelberg, Germany:Springer,2003:17-22.
[45]	ZHANG Y S, PAN M H, HAN Q H, et al. Joint power allocation and route planning scheme for multitarget tracking in airborne radar network under multiuncertainty[J]. IEEE Sensors Journal, 2023, 23(7):7705-7718.
[46]	丁梓航, 谢军伟, 齐铖. 基于强化学习的频控阵-多输入多输出雷达发射功率分配方法[J]. 电子与信息学报, 2023, 45(2):550-557.
	DING Z H, XIE J W, QI C. Transmit power allocation method for frequency controlled array-multiple input multiple output radar based on reinforcement learning[J]. Journal of Electronics and Information Technology, 2023, 45(2):550-557.
[47]	ZHANG H W, XIE J W, SHI J P, et al. Joint beam and waveform selection for the MIMO radar target tracking[J]. Signal Processing, 2019,156:31-40.