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Moving Targets Detection with Low-bit Quantization in Distributed Radar on Moving Platforms
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摘要: 动平台分布式雷达系统可有效提升系统的生存能力和探测性能，但运动平台之间通常采用无线传输方式，难以配备大通信带宽以传输完整的信号数据，给雷达系统的高性能检测带来极大挑战。由于低比特量化技术可显著降低分布式系统的通信传输代价和计算资源消耗，该文针对低信噪比弱信号环境下提出了动平台分布式雷达系统的低比特量化运动目标检测算法。首先，根据系统资源将各节点的多脉冲观测数据选择对应位数的低比特量化器进行量化，推导了关于量化器和多个目标状态的似然函数。其次，证明了低比特量化数据对应似然函数关于未知目标反射系数的凸性，并基于该特性设计了多普勒频移和反射系数的联合估计器。然后，针对探测区域中存在的多个状态未知目标设计了多目标检测器，推导了其恒虚警率门限。最后，通过推导系统的渐近性能设计了最优低比特量化器，在保证系统鲁棒性的同时有效提升了系统的检测性能。仿真实验分析了所提算法的检测与估计性能，结果证明了所提算法在低信噪比弱信号环境下的有效性，同时表明低比特量化数据可在仅占用低于20%通信带宽的基础上实现接近高精度(16比特量化)数据对应的检测和估计性能，且2比特量化策略可作为检测性能和雷达系统资源消耗的折中选择。Abstract: Distributed radar with moving platforms can enhance the survivability and detection performance of a system, however, it is difficult to equip these platforms with sufficient communication bandwidth to transmit high-precision observed data, posing a great challenge to the high-performance detection of a distributed radar system. Because low-bit quantization can effectively reduce the computation cost and resource consumption of distributed radar systems, in this paper, we investigate the high-performance detection of multiple moving targets using the distributed radar system on moving platforms by adopting the low-bit quantization strategy. First, according to system resources, multipulse observed data of each node may be quantized with a low-bit quantizer and the likelihood function relative to the quantizer and states of multiple targets are derived. Subsequently, based on the convexity of the likelihood function relative to the unknown reflection coefficients, a joint estimation algorithm is designed for the Doppler shifts and reflection coefficients. Then, a generalized likelihood ratio test based multi-target detector is designed for detecting multiple targets in the surveillance area with unknown states, and deriving the constant false alarm rate detection threshold. Finally, the optimal low-bit quantizer is designed by deriving the asymptotic detection performance of the system, which effectively improves the detection performance and ensures robustness. Simulation experiments are conducted to analyze the detection and estimation performance of the proposed algorithm, thereby demonstrating the effectiveness of the proposed algorithm for weak signals, and showing that the low-bit quantized data can achieve detection and estimation performance close to that of the high-precision (16-bit quantization) data while consuming a complementary 20% of the communication bandwidth. Besides, according to the simulated results, the two-bit quantization strategy may be a trade-off between the detection performance and resource consumption of the distributed radar system.
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图 1 动平台分布式雷达系统相较于传统固定节点的性能得益示意
Figure 1. Illustration of the performance benefits of a distributed radar system adopting moving platforms compared to the fixed nodes
图 2 分布式雷达系统低比特量化示意图
Figure 2. Schematic of low-bit quantization for distributed radar systems
图 4 1比特、2比特和3比特量化器对应的最优量化门限
Figure 4. Optimal quantization levels for the 1-bit, 2-bit and 3-bit quantizers
图 5 仿真场景示意(箭头表征雷达节点或者目标运动速度)
Figure 5. An illustration of the simulation scenario (arrows represent the velocities of nodes or targets)
图 7 不同量化位数对应各栅格的检测统计量
Figure 7. The test statistic for each grid cell with different quantization bits
图 8 不同量化位数对应的系统性能
Figure 8. System performance corresponding to different quantization bits
图 10 系统针对不同反射强度目标的检测和估计性能
Figure 10. Detection and estimation performance of the system for the targets with different power
1 基于BGDA的联合估计器设计
1. BGDA-based joint estimator design
输入：量化数据$ \widetilde {\boldsymbol{Y}}_l^{\left( q \right)} $，初始状态${\widetilde {\boldsymbol{\alpha}} _{l\mathcal{G}}}\left( 0 \right) = {\left[ {\widetilde \alpha _{l\mathcal{G}}^{\text{R}},\widetilde \alpha _{l\mathcal{G}}^{\text{I}}} \right]^{\rm T} }$，学习率${\beta _l}$，容忍精度${\eta _l}$。 输出：第l个通道的检测统计量$ {\varLambda _{l\mathcal{G}}}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)}} \right) $，未知参数的估计$ \left( {\hat f_l^{\text{d}},{{\hat {\boldsymbol{\alpha}} }_{l\mathcal{G}}}} \right) $。 for $\widetilde f_l^{\text{d}} \in \left[ {f_{\min }^{\text{d}},f_{\max }^{\text{d}}} \right]$ 初始赋值：${\widetilde {\boldsymbol{\alpha }}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right) \leftarrow {\widetilde {\boldsymbol{\alpha }}_{l\mathcal{G}}}\left( 0 \right)$ while ${\left\| {\nabla {{\widetilde \ell }_1}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)};\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right)} \right\|_2} > {\eta _l}$ ${\widetilde {\boldsymbol{\alpha }}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right) \leftarrow {\widetilde {\boldsymbol{\alpha }}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right) + \beta _l^{\rm T} \nabla {\widetilde \ell _1}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)};\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right)$ end $ {\varLambda _{l\mathcal{G}}}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)};\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right) = {\widetilde \ell _1}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)};\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right) $ end $ \left\{ \begin{gathered} \left( {\hat f_l^{\text{d}},{{\hat {\boldsymbol{\alpha}} }_{l\mathcal{G}}}} \right) = \mathop {\arg \max }\limits_{\left\{ {\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right\}} \left\{ {{\varLambda _{l\mathcal{G}}}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)};\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right)} \right\} \\ {\varLambda _{l\mathcal{G}}}\left( {{{\boldsymbol{Y}}_l}} \right) = \max \left\{ {{\varLambda _{l\mathcal{G}}}\left( {\widetilde {\boldsymbol{Y}}_l^{\left( q \right)};\widetilde f_l^{\text{d}},{{\widetilde {\boldsymbol{\alpha }}}_{l\mathcal{G}}}\left( {\widetilde f_l^{\text{d}}} \right)} \right)} \right\} \\ \end{gathered} \right. $ 
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