目标初始距离R0(m) | 距离分辨率ΔR(m) | 速度分辨率Δv(m/s) | 最大可检测距离Rmax(m) | 扫频周期数L |
0<R0<75 | ΔR≤0.1 | Δv≤0.3 | 75 | 512 |
75≤R0≤200 | ΔR≤0.5 | Δv≤1.0 | 200 | 256 |
Citation: | Hongyan WANG, Xiyang XUE, Xiaofeng YANG, Zumin WANG. Joint Design of Millimeter-wave Radar Waveform Parameters and Receiving Weight under Resolution Constraints[J]. Journal of Electronics & Information Technology, 2021, 43(11): 3201-3210. doi: 10.11999/JEIT200978 |
近年来,随着汽车行业快速迭代,毫米波雷达因其成本低、精度高、稳定性好等优点,逐渐成为自动驾驶不可或缺的传感器[1,2]。毫米波雷达发射可设计信号并接收目标回波,而后处理所获得回波以感知环境信息,因而发射信号贯穿于信息获取全过程。通过设计发射信号可改善测量精度及杂波抑制性能从而提升目标检测估计能力进而增强无人驾驶水平,因此,波形设计一直是毫米波雷达领域的研究热点之一[3,4]。
尽管毫米波雷达具有上述显著优势,然而也面临诸如参数估计精度较差以及分辨率较低等问题,为满足自动驾驶对毫米波雷达的高精度高分辨率要求,众多改善雷达检测估计性能的波形设计方法相继被提出[5]。传统调频连续波(Frequency Modulated Continuous Wave, FMCW)信号具有较高距离速度分辨率,然而多目标情况下由于需要目标配对,因而会出现虚假目标[6]。而频移键控(Frequency Shift Keying, FSK)波形可有效避免虚假目标,但是无法确定目标距离方向[7]。针对此问题,文献[8]通过组合FMCW及FSK以消除虚假目标同时提升距离及速度分辨率。基于多频移键控(Multiple Frequency Shift Keying, MFSK)调制,文献[9]设计77 GHz汽车雷达波形以改善多目标检测能力。然而,相较于纯频率测量,基于频率相位测量的MFSK参数估计精度较低。基于此,文献[10]设计具有较短扫频时间的调频序列波形,其基于两次独立频率测量以提高距离速度估计精度。再者,自动驾驶雷达检测近距离目标需要较高距离分辨率,因而需要信号具有大带宽从而须占用大量存储资源[11]。针对此问题,文献[12]提出具有较低调制斜率的双斜率序列,通过组合基于双斜率序列的检测结果以获得较高距离速度分辨率。此外,文献[13]提出带宽可调波形设计方法,其基于最大化输出信杂噪比(Signal-to-Clutter-plus-Noise Ratio, SCNR)准则联合设计可调带宽参数及接收权从而提高目标检测及距离分辨性能。需要注意,雷达距离速度分辨率依赖发射波形参数,且目标检测性能又较大程度上取决于波形参数,因而,可通过设计发射波形参数以改善目标检测及分辨性能进而提升无人驾驶环境感知能力。然而,现有文献较少考虑同时改善目标检测及分辨能力的雷达波形参数设计问题。
针对上述问题,本文提出距离及速度分辨率约束下毫米波雷达波形参数及接收权联合设计方法。首先,所提方法构建基于FMCW信号的目标检测模型;再者,将距离速度分辨率映射至关于发射波形的参数约束;而后,基于最大化输出SCNR准则,构造距离速度分辨率约束下发射波形参数及接收权值联合优化模型;最后,基于交替迭代方法求解所得非线性优化问题。
FMCW雷达由于其结构简单、低成本、高分辨率以及高集成度等特点,广泛应用于自动驾驶领域[14,15]。FMCW信号振幅恒定,频率在扫频周期内线性变化,基于此,第
st(t,l)=exp[j2πf0(t−lT)+jπμ(t−lT)2],t∈[lT,(l+1)T] | (1) |
其中,
假设运动目标相对雷达的径向速度为
sr(t,l)=exp[j2πf0(t−lT−τ)+jπμ(t−lT−τ)2],t∈[lT,(l+1)T] | (2) |
其中,
将回波信号与本地参考信号混频,可得第
sb(t,l)=exp[j2πf0τ+j2πμ(t−lT)τ−jπμτ2] | (3) |
考虑有效区间
sb(t,l)=exp[j2π((2vf0c+μ2(R0+vlT)c)t+2vcμt2+2R0f0c+2vf0lTc)] | (4) |
由式(4)可知,该差拍信号调频带宽为
sb(t,l)=exp[j2π((2vf0c+μ2(R0+vlT)c)t+2R0f0c+2vf0lTc)] | (5) |
基于式(5),差拍信号的第
s(n,l)=exp[j2π((2vf0c+μ2(R0+vlT)c)⋅(n−1)fs+2R0f0c+2vf0lTc)] | (6) |
其中,
s(l)=1NN∑n=1exp[j2π((2vf0c+μ2(R0+vlT)c)⋅(n−1)fs+2R0f0c+2vf0lTc)] | (7) |
毫米波雷达接收阵列由
x(l)=α0a(θ0)s(l)+K∑k=1αka(θk)s(l)+n(l) | (8) |
其中,
基于式(8),可得
x=α0(s⊗IM)a(θ0)+K∑k=1αk(s⊗IM)a(θk)+n | (9) |
其中,
由式(9)可得,波束形成后输出数据可表示为
y=wHα0(s⊗IM)a(θ0)+wHK∑k=1αk(s⊗IM)a(θk)+wHn | (10) |
其中,
众所周知,高斯噪声条件下最大化检测概率可等价为最大化输出SCNR[17]。因此,本文通过最大化输出SCNR以最大化毫米波雷达检测性能。基于式(10),输出SCNR可表示为
SCNR=E[|wHα0(s⊗IM)a(θ0)|2]E[|wHK∑k=1αk(s⊗IM)a(θk)|2]+σ2wHw=snr|wH(s⊗IM)a(θ0)|2wH[(s⊗IM)AΣcAH(s⊗IM)H+ILM]w=snr|wHSa(θ0)|2wH(SAΣcAHSH+ILM)w | (11) |
其中,
由文献[18]可知,FMCW雷达距离分辨率
ΔR=c2B | (12) |
由调制频率
ΔR=c2μT | (13) |
由式(13)可知,
采样频率
Rmax=fscT4B=fsc4μ | (14) |
由式(14)可知,
综上所述,雷达距离分辨率
由文献[20]可知,速度分辨取决于多普勒分辨率,而多普勒分辨率
Δfd=1LT | (15) |
其中,
Δv=Δfdλ2=λ2LT | (16) |
由式(16)可知,
vmax=λ4T | (17) |
由此可得,
综合考虑速度分辨率
由式(11)可知,目标检测性能依赖于接收权及发射信号,而发射信号又取决于调制频率及扫频周期;再者,基于式(12)及式(15),距离速度分辨率又分别由调制频率及扫频周期决定。基于以上所述,可通过联合优化接收权、调制频率及扫频周期改善毫米波雷达检测及速度距离分辨性能,进而提升自动驾驶系统环境感知能力。基于此,速度距离分辨约束下,最大化输出SCNR以提高毫米波雷达检测性能的发射波形及接收权联合优化问题可表述为
maxw,μ,Tsnr|wHSa(θ0)|2wH(SAΣcAHSH+ILM)w,{c/2TΔR≤μ≤fsc/4Rmaxλ/2LΔv≤T≤λ/4vmax | (18) |
由式(18)可知,优化参数
针对上述复杂非线性优化问题,本节基于交替迭代策略进行求解。首先,波形参数
maxwsnr|wHSa(θ0)|2wH(SAΣcAHSH+ILM)w | (19) |
基于最小方差无失真响应(Minimum Variance Distortionless Response, MVDR)准则,式(19)可等价为
minwwH(SAΣcAHSH+ILM)w,wHSa(θ0)=1 | (20) |
由瑞利商定理可知[22],上述问题最优解可表示为
w=(SAΣcAHSH+ILM)−1Sa(θ0)aH(θ0)SH(SAΣcAHSH+ILM)−1Sa(θ0) | (21) |
将式(21)所得最优接收权
snr|wHSa(θ0)|2wH(SAΣcAHSH+ILM)w=aH(θ0)SH(SAΣcAHSH+ILM)−1Sa(θ0) | (22) |
利用矩阵求逆及相关矩阵运算,式(22)可进一步表示为
SCNR=aH(θ0)SH[SRcSH+ILM]−1Sa(θ0)=aH(θ0)SH(ILM−SRc(IM+SHSRc)−1SH)Sa(θ0)=aH(θ0)(SHS−SHSRc(IM+SHSRc)−1SHS)a(θ0)=aH(θ0)(SHS−(IM−(IM+SHSRc)−1)SHS)a(θ0)=aH(θ0)(IM+SHSRc)−1SHSa(θ0)=aH(θ0)((SHS)−1+Rc)−1a(θ0) | (23) |
其中,
由于
SHS=sHs⊗IM=L∑l=1(1NN∑n=1exp[j2π((2vf0c+μ2(R0+vlT)c)(n−1)fs+2R0f0c+2vf0lTc)]×1NN∑m=1exp[j2π((2vf0c+μ2(R0+vlT)c)(m−1)fs+2R0f0c+2vf0lTc)])⊗IM=1N2L∑l=1N∑n=1N∑m=1exp[j2π(2vf0c+μ2(R0+vlT)c)(m−n)fs]⊗IM=C(μ,T)IM | (24) |
其中,
SCNR=aH(θ0)(C−1(μ,T)IM+Rc)−1a(θ0) | (25) |
将式(25)代入式(18),关于调制频率
maxμ,TaH(θ0)(C−1(μ,T)+Rc)−1a(θ0),c/2TΔR≤μ≤fsc/4Rmax,λ/2LΔv≤T≤λ/4vmax | (26) |
在扫频周期
maxμaH(θ0)(C(μ,T)−1+Rc)−1a(θ0),c/2TΔR≤μ≤fsc/4Rmax | (27) |
将式(27)所得最优调制频率
maxTaH(θ0)(C(μ,T)−1+Rc)−1a(θ0),λ/2LΔv≤T≤λ/4vmax | (28) |
由式(24)可得,
基于以上讨论,固定发射波形参数
(1)求解式(21)以获得最优接收权
(2)求解式(27)获得最优调制频率
(3)求解式(28)获得最优扫频周期
(4)重复迭代步骤(1)—步骤(3),直至满足如下准则:
通过上述算法,可获得最优波形参数
远近距离场景下,通过与未优化FMCW对比,并逐次分析接收权、调制频率以及扫频周期对输出SCNR之影响,以验证所提算法的有效性。实验环境如下:仿真软件为MATLAB R2016a,处理器为Intel i7-7700,主频为4 GHz,内存为8 GB。仿真条件如下:接收阵元数
目标初始距离R0(m) | 距离分辨率ΔR(m) | 速度分辨率Δv(m/s) | 最大可检测距离Rmax(m) | 扫频周期数L |
0<R0<75 | ΔR≤0.1 | Δv≤0.3 | 75 | 512 |
75≤R0≤200 | ΔR≤0.5 | Δv≤1.0 | 200 | 256 |
实验1 考虑如下场景:目标初始距离
BeamPattern(θ)=|wHSa(θ0)| | (29) |
图1为所提算法及未优化FMCW所得波束方向图。由图1可知,所提算法在
实验2 目标初始距离
实验3 目标初始距离分别为
实验4 目标初始距离分别为
实验5 目标初始距离
实验6 目标初始距离
为改善自动驾驶中毫米波雷达目标检测及分辨性能,本文提出一种分辨率约束下提升毫米波雷达目标检测概率的波形参数及接收权联合设计方法。所提方法首先基于FMCW信号构建毫米波雷达检测模型,而后在分析目标距离速度分辨率与发射波形参数关系的基础上,基于最大化SCNR准则构造距离及速度分辨约束下发射波形参数及接收权值联合优化模型,最后利用交替迭代方法求解所得非线性优化问题。仿真结果表明,远近不同距离及不同杂波场景下,相较于参数未优化的FMCW,所提方法均可显著改善目标检测性能,同时满足给定距离及速度分辨需求。
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目标初始距离R0(m) | 距离分辨率ΔR(m) | 速度分辨率Δv(m/s) | 最大可检测距离Rmax(m) | 扫频周期数L |
0<R0<75 | ΔR≤0.1 | Δv≤0.3 | 75 | 512 |
75≤R0≤200 | ΔR≤0.5 | Δv≤1.0 | 200 | 256 |