该雷达的工作原理如　下:　毫米波雷达传感器基础知识　1　2　3　4　IF　‫ؗ‬ਭ　ਾᡆಞ　TX　ཟ㓵RX　ཟ㓵　␭仇ಞ　图3.FMCW　雷达框图。　Figure　2.　Chirp　signal,　with　frequency　as　a　function　of　time.　An　FMCW　radar　system　transmits　a　chirp　signal　and　captures　the　signals　reflected　by　objects　in　its　path.　Fi　represents　a　simplified　block　diagram　of　the　main　RF　components　of　a　FMCW　radar.　The　radar　operates　as　•　A　synthesizer　(synth)　generates　a　chirp.　•　The　chirp　is　transmitted　by　a　transmit　antenna　(TX　ant).　•　The　reflection　of　the　chirp　by　an　object　generates　a　reflected　chirp　captured　by　the　receive　antenn　•　A　“mixer”　combines　the　RX　and　TX　signals　to　produce　an　intermediate　frequency　(IF)　signal.　Figure　3.　FMCW　radar　block　diagram.　A　frequency　mixer　is　an　electronic　component　that　combines　two　signals　to　create　a　new　signal　with　a　new　For　two　sinusoidal　inputs　x1　and　x2　(Equations　1　and　2):　\ud835\udc65\ud835\udc651　=　sin(\ud835\udf14\ud835\udf141\ud835\udc61\ud835\udc61　+　\ud835\udef7\ud835\udef71)　(1)　\ud835\udc65\ud835\udc652　=　sin(\ud835\udf14\ud835\udf142\ud835\udc61\ud835\udc61　+　\ud835\udef7\ud835\udef72)　(2)　The　output　xout　has　an　instantaneous　frequency　equal　to　the　difference　of　the　instantaneous　frequencies　o　input　sinusoids.　The　phase　of　the　output　xout　is　equal　to　the　difference　of　the　phases　of　the　two　input　signa　3):　\ud835\udc65\ud835\udc65\ud835\udc5c\ud835\udc5c\ud835\udc5c\ud835\udc5c\ud835\udc5c\ud835\udc5c　=　sin[(\ud835\udf14\ud835\udf141　−　\ud835\udf14\ud835\udf142)\ud835\udc61\ud835\udc61　+　(\ud835\udef7\ud835\udef71　−　\ud835\udef7\ud835\udef72)]　(3)　The　operation　of　the　frequency　mixer　can　also　be　understood　graphically　by　looking　at　TX　and　RX　chirp　fre　representation　as　a　function　of　time.　Figure　2.　Chirp　signal,　with　frequency　as　a　function　of　time.　An　FMCW　radar　system　transmits　a　chirp　signal　and　captures　the　signals　reflected　by　objects　in　its　path.　F　represents　a　simplified　block　diagram　of　the　main　RF　components　of　a　FMCW　radar.　The　radar　operates　a　•　A　synthesizer　(synth)　generates　a　chirp.　•　The　chirp　is　transmitted　by　a　transmit　antenna　(TX　ant).　•　The　reflection　of　the　chirp　by　an　object　generates　a　reflected　chirp　captured　by　the　receive　anten　•　A　“mixer”　combines　the　RX　and　TX　signals　to　produce　an　intermediate　frequency　(IF)　signal.　Figure　3.　FMCW　radar　block　diagram.　A　frequency　mixer　is　an　electronic　component　that　combines　two　signals　to　create　a　new　signal　with　a　ne　For　two　sinusoidal　inputs　x1　and　x2　(Equations　1　and　2):　\ud835\udc65\ud835\udc651　=　sin(\ud835\udf14\ud835\udf141\ud835\udc61\ud835\udc61　+　\ud835\udef7\ud835\udef71)　(1)　\ud835\udc65\ud835\udc652　=　sin(\ud835\udf14\ud835\udf142\ud835\udc61\ud835\udc61　+　\ud835\udef7\ud835\udef72)　(2)　The　output　xout　has　an　instantaneous　frequency　equal　to　the　difference　of　the　instantaneous　frequencies　input　sinusoids.　The　phase　of　the　output　xout　is　equal　to　the　difference　of　the　phases　of　the　two　input　sign　3):　\ud835\udc65\ud835\udc65\ud835\udc5c\ud835\udc5c\ud835\udc5c\ud835\udc5c\ud835\udc5c\ud835\udc5c　=　sin[(\ud835\udf14\ud835\udf141　−　\ud835\udf14\ud835\udf142)\ud835\udc61\ud835\udc61　+　(\ud835\udef7\ud835\udef71　−　\ud835\udef7\ud835\udef72)]　(3)　The　operation　of　the　frequency　mixer　can　also　be　understood　graphically　by　looking　at　TX　and　RX　chirp　fr　representation　as　a　function　of　time.　毫米波雷达传感器基础知识　	　4	　2017　年5月延时　(t)　可通过数学方法推导出方程式　4:　(4)　其中　d　是与被检测物体的距离,c　是光速。　要获取混频器输出处作为　IF　信号时间函数的频率　表示法,只要去掉图　4　上半部分中显示的两条线即　可。这两条线之间的距离是固定的,这表示　IF　信号　包含一个频率恒定的单音信号。图4显示该频率为　St。IF　信号仅在　TX　线性调频脉冲和　RX　线性调频　脉冲重叠的时段(即图　4　中垂直虚线之间的时段)　有效。　混频器输出信号作为时间的幅度函数是一个正弦　波,因为它有恒定频率。　IF　信号的初始相位　(F0)　是IF　信号起点对应的时间　点(即图　4　中左侧垂直虚线表示的时间点)的TX　线性调频脉冲相位与　RX　线性调频脉冲相位之差。　(方程式　5):　(5)　通过数学方法,它可以进一步导入方程式　6:　(6)*　总之,对于与雷达的距离为　d　的物体,IF　信号将是　一个正弦波(方程式　7),因此:　(7)**　其中　和。在本介绍性白皮书中,我们忽略　IF　信号的频率与　物体速度的依赖关系。在快速　FMCW　雷达中,其　影响通常非常小,且在处理完成多普勒　FFT　后,即　可轻松对其进行进一步校正。上述分析均假设雷达　仅检测到一个物体。让我们来分析一个检测到若干　物体的情形。图5显示了接收自不同物体的三个不　同的　RX　线性调频脉冲。每个线性调频脉冲的延时　都不一样,延时和与该物体的距离成正比。不同的　RX　线性调频脉冲转化为多个　IF　单音信号,每个信　号频率恒定。　t　t　f　f　TX　㓵ᙝ　䈹仇㜿ߨ　RX　㓵ᙝ　䈹仇㜿ߨ　IF　‫ؗ‬ਭ　Tc　S　S　图4.IF　频率恒定不变。　per　diagram　in　Figure　4　shows　TX　and　RX　chirps　as　a　function　of　time　for　a　single　object　detected.　Notice　that　the　p　is　a　time-delay　version　of　the　TX　chirp.　e　delay　(τ)　can　be　mathematically　derived　as　Equation　4:　\ud835\udf0f\ud835\udf0f　=　2\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　(5)　d　is　the　distance　to　the　detected　object　and　c　is　the　speed　of　light.　in　the　frequency　representation　as　a　function　of　time　of　the　IF　signal　at　the　output　of　the　frequency　mixer,　t　the　two　lines　presented　in　the　upper　section　of　Figure　4.　The　distance　between　the　two　lines　is　fixed,　which　that　the　IF　signal　consists　of　a　tone　with　a　constant　frequency.　Figure　4　shows　that　this　frequency　is　Sτ.　The　IF　valid　only　in　the　time　interval　where　both　the　TX　chirp　and　the　RX　chirp　overlap　(i.e.,　the　interval　between　the　dotted　lines　in　Figure　4)　.　Figure　4.　IF　frequency　is　constant.　er　output　signal　as　a　magnitude　function　of　time　is　a　sine　wave,　since　it　has　a　constant　frequency.　ial　phase　of　the　IF　signal　(Φ0)　is　the　difference　between　the　phase　of　the　TX　chirp　and　the　phase　of　the　RX　chirp　me　instant　corresponding　to　the　start　of　the　IF　signal　(i.e.,　the　time　instant　represented　by　the　left　vertical　dotted　igure　4).　(Equation　5):　\ud835\udf19\ud835\udf190　=　2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc50\ud835\udc50\ud835\udf0f\ud835\udf0f　(5)　matically,　it　can　be　further　derived　into　Equation　6:　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　(6)　mary,　for　an　object　at　a　distance　d　from　the　radar,　the　IF　signal　will　be　a　sine　wave　(Equation　7),　then:　\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34(2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc5c\ud835\udc5c\ud835\udc61\ud835\udc61　+　\ud835\udf19\ud835\udf190)　(7)　\ud835\udc53\ud835\udc530　=　\ud835\udc46\ud835\udc462\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　and　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　.　umption　so　far　is　that　the　radar　has　detected　only　one　object.　Let’s　analyze　a　case　when　there　are　several　objects　d.　Figure　5　shows　three　different　RX　chirps　received　from　different　objects.　Each　chirp　is　delayed　by　a　different　The　initial　phase　of　the　IF　signal　(Φ0)　is　the　difference　between　the　phase　of　the　TX　chirp　and　the　ph　at　the　time　instant　corresponding　to　the　start　of　the　IF　signal　(i.e.,　the　time　instant　represented　by　th　line　in　Figure　4).　(Equation　5):　\ud835\udf19\ud835\udf190　=　2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc50\ud835\udc50\ud835\udf0f\ud835\udf0f　(5)　Mathematically,　it　can　be　further　derived　into　Equation　6:　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　(6)　In　summary,　for　an　object　at　a　distance　d　from　the　radar,　the　IF　signal　will　be　a　sine　wave　(Equation　7　\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34(2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc5c\ud835\udc5c\ud835\udc61\ud835\udc61　+　\ud835\udf19\ud835\udf190)　(7)　where　\ud835\udc53\ud835\udc530　=　\ud835\udc46\ud835\udc462\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　and　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　.　The　assumption　so　far　is　that　the　radar　has　detected　only　one　object.　Let’s　analyze　a　case　when　ther　detected.　Figure　5　shows　three　different　RX　chirps　received　from　different　objects.　Each　chirp　is　dela　The　initial　phase　of　the　IF　signal　(Φ0)　is　the　difference　between　the　phase　of　the　TX　chirp　and　the　p　at　the　time　instant　corresponding　to　the　start　of　the　IF　signal　(i.e.,　the　time　instant　represented　by　t　line　in　Figure　4).　(Equation　5):　\ud835\udf19\ud835\udf190　=　2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc50\ud835\udc50\ud835\udf0f\ud835\udf0f　(5)　Mathematically,　it　can　be　further　derived　into　Equation　6:　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　(6)　In　summary,　for　an　object　at　a　distance　d　from　the　radar,　the　IF　signal　will　be　a　sine　wave　(Equation　\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34(2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc5c\ud835\udc5c\ud835\udc61\ud835\udc61　+　\ud835\udf19\ud835\udf190)　(7)　where　\ud835\udc53\ud835\udc530　=　\ud835\udc46\ud835\udc462\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　and　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　.　The　assumption　so　far　is　that　the　radar　has　detected　only　one　object.　Let’s　analyze　a　case　when　ther　detected.　Figure　5　shows　three　different　RX　chirps　received　from　different　objects.　Each　chirp　is　del　The　initial　phase　of　the　IF　signal　(Φ0)　is　the　difference　between　the　phase　at　the　time　instant　corresponding　to　the　start　of　the　IF　signal　(i.e.,　the　tim　line　in　Figure　4).　(Equation　5):　\ud835\udf19\ud835\udf190　=　2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc50\ud835\udc50\ud835\udf0f\ud835\udf0f　(5　Mathematically,　it　can　be　further　derived　into　Equation　6:　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　(6　In　summary,　for　an　object　at　a　distance　d　from　the　radar,　the　IF　signal　will　\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34(2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc5c\ud835\udc5c\ud835\udc61\ud835\udc61　+　\ud835\udf19\ud835\udf190)　where　\ud835\udc53\ud835\udc530　=　\ud835\udc46\ud835\udc462\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　and　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　.　The　assumption　so　far　is　that　the　radar　has　detected　only　one　object.　Let’　detected.　Figure　5　shows　three　different　RX　chirps　received　from　differen　The　initial　phase　of　the　IF　signal　(Φ0)　is　the　difference　between　the　phas　at　the　time　instant　corresponding　to　the　start　of　the　IF　signal　(i.e.,　the　tim　line　in　Figure　4).　(Equation　5):　\ud835\udf19\ud835\udf190　=　2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc50\ud835\udc50\ud835\udf0f\ud835\udf0f　(　Mathematically,　it　can　be　further　derived　into　Equation　6:　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　(　In　summary,　for　an　object　at　a　distance　d　from　the　radar,　the　IF　signal　wi　\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34(2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc5c\ud835\udc5c\ud835\udc61\ud835\udc61　+　\ud835\udf19\ud835\udf190)　where　\ud835\udc53\ud835\udc530　=　\ud835\udc46\ud835\udc462\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　and　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　.　The　assumption　so　far　is　that　the　radar　has　detected　only　one　object.　Let　detected.　Figure　5　shows　three　different　RX　chirps　received　from　differe　f　f　TX　㓵ᙝ　᧛᭬㠠ཐѠ⢟։Ⲻ　ਃሺ‫ؗ‬ਭ　t　t　图5.针对多个物体检测发射的多个　IF　单音信号。　gram　in　Figure　4　shows　TX　and　RX　chirps　as　a　function　of　time　for　a　single　object　detected.　Notice　that　the　me-delay　version　of　the　TX　chirp.　(τ)　can　be　mathematically　derived　as　Equation　4:　\ud835\udf0f\ud835\udf0f　=　2\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　(5)　distance　to　the　detected　object　and　c　is　the　speed　of　light.　requency　representation　as　a　function　of　time　of　the　IF　signal　at　the　output　of　the　frequency　mixer,　wo　lines　presented　in　the　upper　section　of　Figure　4.　The　distance　between　the　two　lines　is　fixed,　which　e　IF　signal　consists　of　a　tone　with　a　constant　frequency.　Figure　4　shows　that　this　frequency　is　Sτ.　The　IF　nly　in　the　time　interval　where　both　the　TX　chirp　and　the　RX　chirp　overlap　(i.e.,　the　interval　between　the　lines　in　Figure　4)　.　Figure　4.　IF　frequency　is　constant.　put　signal　as　a　magnitude　function　of　time　is　a　sine　wave,　since　it　has　a　constant　frequency.　se　of　the　IF　signal　(Φ0)　is　the　difference　between　the　phase　of　the　TX　chirp　and　the　phase　of　the　RX　chirp　tant　corresponding　to　the　start　of　the　IF　signal　(i.e.,　the　time　instant　represented　by　the　left　vertical　dotted　).　(Equation　5):　\ud835\udf19\ud835\udf190　=　2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc50\ud835\udc50\ud835\udf0f\ud835\udf0f　(5)　y,　it　can　be　further　derived　into　Equation　6:　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　(6)　or　an　object　at　a　distance　d　from　the　radar,　the　IF　signal　will　be　a　sine　wave　(Equation　7),　then:　\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34\ud835\udc34(2\ud835\udf0b\ud835\udf0b\ud835\udc53\ud835\udc53\ud835\udc5c\ud835\udc5c\ud835\udc61\ud835\udc61　+　\ud835\udf19\ud835\udf190)　(7)　\ud835\udc51\ud835\udc51　and　\ud835\udf19\ud835\udf190　=　4\ud835\udf0b\ud835\udf0b\ud835\udc51\ud835\udc51　\ud835\udf06\ud835\udf06　.　n　so　far　is　that　the　radar　has　detected　only　one　object.　Let’s　analyze　a　case　when　there　are　several　objects　re　5　shows　three　different　RX　chirps　received　from　different　objects.　Each　chirp　is　delayed　by　a　different　*　　该方程式是一个近似等式,仅在斜率和距离足够小时才　有效。不过,IF　信号的相位与很小的距离变化呈线性关　系(即Δf=4πΔd/l)仍然是正确的。　**　　在本介绍性白皮书中,我们忽略　IF　信号的频率与物体　速度的依赖关系。在快速　FMCW　雷达中,其影响通常　非常小,且在处理完成多普勒　FFT　后,即可轻松对其　进行进一步校正。　毫米波雷达传感器基础知识　	　5	　2017　年5月这个包含多个单音信号的　IF　信号必须使用傅里叶变　换加以处理,以便分离不同的-单音。傅里叶变换处　理将会产生一个具有不同的分离峰值的频谱,每个　峰值表示在特定距离处存在物体。　距离分辨率　距离分辨率是辨别两个或更多物体的能力。当两个　物体靠近到某个位置时,雷达系统将不再能够将二　者区分开物体。傅里叶变换理论指出,通过延长　IF　信号,可以提高分辨率。　要延长　IF　信号,还必须按比例增加带宽。延长的　IF　信号会产生一个有两个分离峰值的　IF　谱。　傅里叶变换理论还指出,观测窗口　(T)　可以分辨间　隔超过　1/THz　的频率分量。这意味着只要频率差满　足方程式　8　中给出的关系,就可以分辨两个　IF　单　音信号的　(8)　其中　Tc　是观测时间长度。　由于　方程式　8　可以表达为　(由于　B　=　STc)。　距离分辨率　(dRes)　仅取决于线性调频脉冲扫频的带　宽(方程式　9):　(9)　因此,　线性调频脉冲带宽为数　GHz　的FMCW　雷达　将有约为数厘米的距离分辨率　(例如,　4GHz　的线性　调频脉冲带宽可转化为　3.75cm　的距离分辨率)　。　速度测量　在本节中,让我们使用相量表示(距离、角度)来　求一个复数。　使用两个线性调频脉冲进行的速度测量　为了测量速度,FMCW　雷达会发射两个间隔　Tc　的　线性调频脉冲。每个反射的线性调频脉冲通过　FFT　加以处理,以便检测物体的距离(距离　FFT)。对　应于每个线性调频脉冲的距离　FFT　将在同一位置出　现峰值,但相位不同。该测得的相位差对应于速度　为vTc　的物体的移动。　相位差通过方程式　6　推导出方程式　10:　(10)　可以使用方程式　11　推导速度:　(11)　由于速度测量基于相位差,因而会存在模糊性。这　种测量仅在　|DF|<　p　时具有非模糊性。使用上述方　程式　11　可通过数学方法推导出　。　方程式　12　给出由间隔　Tc　的两个线性调频脉冲可以　测得的最大相对速度　(vmax)。更高的　vmax　需要两个　线性调频脉冲之间更短的传输时间。　Tc　图6.双线性调频脉冲速度测量。　Figure　5.　Multiple　IF　tones　for　multiple-object　detection.　F　signal　consisting　of　multiple　tones　must　be　processed　using　a　Fourier　transform　in　order　to　separate　the　different　.　Fourier　transform　processing　will　result　in　a　frequency　spectrum　that　has　separate　peaks　for　the　different　tones　peak　denoting　the　presence　of　an　object　at　a　specific　distance.　e　Resolution　e　resolution　is　the　ability　to　distinguish　between　two　or　more　objects.　When　two　objects　move　closer,　at　some　,　a　radar　system　will　no　longer　be　able　to　distinguish　them　as　separate　objects.　Fourier　transform　theory　states　that　an　increase　the　resolution　by　increasing　the　length　of　the　IF　signal.　crease　the　length　of　the　IF　signal,　the　bandwidth　must　also　be　increased　proportionally.　An　increased-length　IF　results　in　an　IF　spectrum　with　two　separate　peaks.　er　transform　theory　also　states　that　an　observation　window　(T)　can　resolve　frequency　components　that　are　ated　by　more　than　1/THz.　This　means　that　two　IF　signal　tones　can　be　resolved　in　frequency　as　long　as　the　ency　difference　satisfies　the　relationship　given　in　Equation　8:　Δ\ud835\udc53\ud835\udc53　>　1　\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(8)　e　Tc　is　the　observation　interval.　Δ\ud835\udc53\ud835\udc53　=　\ud835\udc46\ud835\udc462Δ\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　,　equation　(8)　can　be　expressed　as　Δ\ud835\udc51\ud835\udc51　>　\ud835\udc50\ud835\udc50　2\ud835\udc46\ud835\udc46\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(since　B　=　STc　).　ange　resolution　(dRes)　depends　only　on　the　bandwidth　swept　by　the　chirp　(Equation　9):　\ud835\udc51\ud835\udc51\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(9)　an　FMCW　radar　with　a　chirp　bandwidth　of　a　few　GHz　will　have　a　range　resolution　in　the　order　of　cm's　(e.g.　a　chirp　width　of　4GHz　translates　to　a　range　resolution　3.75cm)　Figure　5.　Multiple　IF　tones　for　multiple-object　detection.　This　IF　signal　consisting　of　multiple　tones　must　be　processed　using　a　Fourier　transform　in　order　to　separate　the　different　tones.　Fourier　transform　processing　will　result　in　a　frequency　spectrum　that　has　separate　peaks　for　the　different　tones　each　peak　denoting　the　presence　of　an　object　at　a　specific　distance.　Range　Resolution　Range　resolution　is　the　ability　to　distinguish　between　two　or　more　objects.　When　two　objects　move　closer,　at　some　point,　a　radar　system　will　no　longer　be　able　to　distinguish　them　as　separate　objects.　Fourier　transform　theory　states　that　you　can　increase　the　resolution　by　increasing　the　length　of　the　IF　signal.　To　increase　the　length　of　the　IF　signal,　the　bandwidth　must　also　be　increased　proportionally.　An　increased-length　IF　signal　results　in　an　IF　spectrum　with　two　separate　peaks.　Fourier　transform　theory　also　states　that　an　observation　window　(T)　can　resolve　frequency　components　that　are　separated　by　more　than　1/THz.　This　means　that　two　IF　signal　tones　can　be　resolved　in　frequency　as　long　as　the　frequency　difference　satisfies　the　relationship　given　in　Equation　8:　Δ\ud835\udc53\ud835\udc53　>　1　\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(8)　where　Tc　is　the　observation　interval.　Since　Δ\ud835\udc53\ud835\udc53　=　\ud835\udc46\ud835\udc462Δ\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　,　equation　(8)　can　be　expressed　as　Δ\ud835\udc51\ud835\udc51　>　\ud835\udc50\ud835\udc50　2\ud835\udc46\ud835\udc46\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(since　B　=　STc　).　The　range　resolution　(dRes)　depends　only　on　the　bandwidth　swept　by　the　chirp　(Equation　9):　\ud835\udc51\ud835\udc51\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(9)　Thus　an　FMCW　radar　with　a　chirp　bandwidth　of　a　few　GHz　will　have　a　range　resolution　in　the　order　of　cm's　(e.g.　a　chirp　bandwidth　of　4GHz　translates　to　a　range　resolution　3.75cm)　gure　5.　Multiple　IF　tones　for　multiple-object　detection.　e　tones　must　be　processed　using　a　Fourier　transform　in　order　to　separate　the　different　ng　will　result　in　a　frequency　spectrum　that　has　separate　peaks　for　the　different　tones　of　an　object　at　a　specific　distance.　istinguish　between　two　or　more　objects.　When　two　objects　move　closer,　at　some　r　be　able　to　distinguish　them　as　separate　objects.　Fourier　transform　theory　states　that　increasing　the　length　of　the　IF　signal.　nal,　the　bandwidth　must　also　be　increased　proportionally.　An　increased-length　IF　h　two　separate　peaks.　es　that　an　observation　window　(T)　can　resolve　frequency　components　that　are　is　means　that　two　IF　signal　tones　can　be　resolved　in　frequency　as　long　as　the　relationship　given　in　Equation　8:　Δ\ud835\udc53\ud835\udc53　>　1　\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(8)　al.　n　be　expressed　as　Δ\ud835\udc51\ud835\udc51　>　\ud835\udc50\ud835\udc50　2\ud835\udc46\ud835\udc46\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(since　B　=　STc　).　ds　only　on　the　bandwidth　swept　by　the　chirp　(Equation　9):　\ud835\udc51\ud835\udc51\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(9)　bandwidth　of　a　few　GHz　will　have　a　range　resolution　in　the　order　of　cm's　(e.g.　a　chirp　a　range　resolution　3.75cm)　Figure　5.　Multiple　IF　tones　for　multiple-object　detection.　signal　consisting　of　multiple　tones　must　be　processed　using　a　Fourier　transform　in　order　to　separate　the　different　Fourier　transform　processing　will　result　in　a　frequency　spectrum　that　has　separate　peaks　for　the　different　tones　eak　denoting　the　presence　of　an　object　at　a　specific　distance.　Resolution　esolution　is　the　ability　to　distinguish　between　two　or　more　objects.　When　two　objects　move　closer,　at　some　radar　system　will　no　longer　be　able　to　distinguish　them　as　separate　objects.　Fourier　transform　theory　states　that　increase　the　resolution　by　increasing　the　length　of　the　IF　signal.　ease　the　length　of　the　IF　signal,　the　bandwidth　must　also　be　increased　proportionally.　An　increased-length　IF　esults　in　an　IF　spectrum　with　two　separate　peaks.　transform　theory　also　states　that　an　observation　window　(T)　can　resolve　frequency　components　that　are　ed　by　more　than　1/THz.　This　means　that　two　IF　signal　tones　can　be　resolved　in　frequency　as　long　as　the　ncy　difference　satisfies　the　relationship　given　in　Equation　8:　Δ\ud835\udc53\ud835\udc53　>　1　\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(8)　Tc　is　the　observation　interval.　\ud835\udc53\ud835\udc53　=　\ud835\udc46\ud835\udc462Δ\ud835\udc51\ud835\udc51　\ud835\udc50\ud835\udc50　,　equation　(8)　can　be　expressed　as　Δ\ud835\udc51\ud835\udc51　>　\ud835\udc50\ud835\udc50　2\ud835\udc46\ud835\udc46\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(since　B　=　STc　).　ge　resolution　(dRes)　depends　only　on　the　bandwidth　swept　by　the　chirp　(Equation　9):　\ud835\udc51\ud835\udc51\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45\ud835\udc45　=　\ud835\udc50\ud835\udc50　2\ud835\udc35\ud835\udc35　(9)　FMCW　radar　with　a　chirp　bandwidth　of　a　few　GHz　will　have　a　range　resolution　in　the　order　of　cm's　(e.g.　a　chirp　dth　of　4GHz　translates　to　a　range　resolution　3.75cm)　Velocity　Measurement　In　this　section,　let’s　use　phasor　notation　(distance,　angle)　for　a　complex　number.　Velocity　Measurement　with　Two　Chirps　In　order　to　measure　velocity,　a　FMCW　radar　transmits　two　chirps　separated　by　Tc　Each　reflected　chir　through　FFT　to　detect　the　range　of　the　object　(range-FFT).　The　range-FFT　corresponding　to　each　chir　the　same　location,　but　with　a　different　phase.　The　measured　phase　difference　corresponds　to　a　mot　vTc.　Figure　6.　Two-chirp　velocity　measurement.　The　phase　difference　is　defined　as　Equation　10:　∆\ud835\udef7\ud835\udef7　=　4\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　\ud835\udf06\ud835\udf06　(10)　You　can　derive　the　velocity　using　Equation　11:　\ud835\udc63\ud835\udc63　=　\ud835\udf06\ud835\udf06Δ\ud835\udef7\ud835\udef7　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(11)　Since　the　velocity　measurement　is　based　on　a　phase　difference,　there　will　be　ambiguity.　The　measur　unambiguous　only　if　|∆\ud835\udef7\ud835\udef7|<　π.　Using　equation　11　above,　one　can　mathematically　derive　\ud835\udc63\ud835\udc63　<　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　.　Equation　12　provides　the　maximum　relative　speed　(vmax)　measured　by　two　chirps　spaced　Tc　apart.　Hi　shorter　transmission　times　between　chirps.　vmax　=　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(12)　Velocity　Measurement　with　Multiple　Objects　at　the　Same　Range　The　two-chirp　velocity　measurement　method　does　not　work　if　multiple　moving　objects　with　differen　the　time　of　measurement,　both　at　the　same　distance　from　the　radar.　Since　these　objects　are　at　the　s　will　generate　reflective　chirps　with　identical　IF　frequencies.　As　a　consequence,　the　range-FFT　will　res　which　represents　the　combined　signal　from　all　of　these　equi-range　objects.　A　simple　phase　comparis　not　work.　Velocity　Measurement　In　this　section,　let’s　use　phasor　notation　(distance,　angle)　for　a　complex　number.　Velocity　Measurement　with　Two　Chirps　In　order　to　measure　velocity,　a　FMCW　radar　transmits　two　chirps　separated　by　Tc　Each　reflected　ch　through　FFT　to　detect　the　range　of　the　object　(range-FFT).　The　range-FFT　corresponding　to　each　ch　the　same　location,　but　with　a　different　phase.　The　measured　phase　difference　corresponds　to　a　m　vTc.　Figure　6.　Two-chirp　velocity　measurement.　The　phase　difference　is　defined　as　Equation　10:　∆\ud835\udef7\ud835\udef7　=　4\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　\ud835\udf06\ud835\udf06　(10)　You　can　derive　the　velocity　using　Equation　11:　\ud835\udc63\ud835\udc63　=　\ud835\udf06\ud835\udf06Δ\ud835\udef7\ud835\udef7　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(11)　Since　the　velocity　measurement　is　based　on　a　phase　difference,　there　will　be　ambiguity.　The　meas　unambiguous　only　if　|∆\ud835\udef7\ud835\udef7|<　π.　Using　equation　11　above,　one　can　mathematically　derive　\ud835\udc63\ud835\udc63　<　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　.　Equation　12　provides　the　maximum　relative　speed　(vmax)　measured　by　two　chirps　spaced　Tc　apart.　shorter　transmission　times　between　chirps.　vmax　=　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(12)　Velocity　Measurement　with　Multiple　Objects　at　the　Same　Range　The　two-chirp　velocity　measurement　method　does　not　work　if　multiple　moving　objects　with　differ　the　time　of　measurement,　both　at　the　same　distance　from　the　radar.　Since　these　objects　are　at　th　will　generate　reflective　chirps　with　identical　IF　frequencies.　As　a　consequence,　the　range-FFT　will　r　which　represents　the　combined　signal　from　all　of　these　equi-range　objects.　A　simple　phase　compa　not　work.　Velocity　Measurement　In　this　section,　let’s　use　phasor　notation　(distance,　angle)　for　a　complex　number.　Velocity　Measurement　with　Two　Chirps　In　order　to　measure　velocity,　a　FMCW　radar　transmits　two　chirps　separated　by　Tc　Each　reflected　chirp　is　processed　through　FFT　to　detect　the　range　of　the　object　(range-FFT).　The　range-FFT　corresponding　to　each　chirp　will　have　peaks　in　the　same　location,　but　with　a　different　phase.　The　measured　phase　difference　corresponds　to　a　motion　in　the　object　of　vTc.　Figure　6.　Two-chirp　velocity　measurement.　The　phase　difference　is　defined　as　Equation　10:　∆\ud835\udef7\ud835\udef7　=　4\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　\ud835\udf06\ud835\udf06　(10)　You　can　derive　the　velocity　using　Equation　11:　\ud835\udc63\ud835\udc63　=　\ud835\udf06\ud835\udf06Δ\ud835\udef7\ud835\udef7　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(11)　Since　the　velocity　measurement　is　based　on　a　phase　difference,　there　will　be　ambiguity.　The　measurement　is　unambiguous　only　if　|∆\ud835\udef7\ud835\udef7|<　π.　Using　equation　11　above,　one　can　mathematically　derive　\ud835\udc63\ud835\udc63　<　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　.　Equation　12　provides　the　maximum　relative　speed　(vmax)　measured　by　two　chirps　spaced　Tc　apart.　Higher　vmax　requires　shorter　transmission　times　between　chirps.　vmax　=　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(12)　Velocity　Measurement　with　Multiple　Objects　at　the　Same　Range　The　two-chirp　velocity　measurement　method　does　not　work　if　multiple　moving　objects　with　different　velocities　are　at　the　time　of　measurement,　both　at　the　same　distance　from　the　radar.　Since　these　objects　are　at　the　same　distance,　they　will　generate　reflective　chirps　with　identical　IF　frequencies.　As　a　consequence,　the　range-FFT　will　result　in　single　peak,　which　represents　the　combined　signal　from　all　of　these　equi-range　objects.　A　simple　phase　comparison　technique　will　not　work.　Figure　6.　Two-chirp　velocity　measurement.　The　phase　difference　is　defined　as　Equation　10:　∆\ud835\udef7\ud835\udef7　=　4\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　\ud835\udf06\ud835\udf06　(10)　You　can　derive　the　velocity　using　Equation　11:　\ud835\udc63\ud835\udc63　=　\ud835\udf06\ud835\udf06Δ\ud835\udef7\ud835\udef7　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(11)　Since　the　velocity　measurement　is　based　on　a　phase　difference,　there　will　be　ambiguity.　The　measu　unambiguous　only　if　|∆\ud835\udef7\ud835\udef7|<　π.　Using　equation　11　above,　one　can　mathematically　derive　\ud835\udc63\ud835\udc63　<　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　.　Equation　12　provides　the　maximum　relative　speed　(vmax)　measured　by　two　chirps　spaced　Tc　apart.　H　shorter　transmission　times　between　chirps.　vmax　=　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(12)　Velocity　Measurement　with　Multiple　Objects　at　the　Same　Range　The　two-chirp　velocity　measurement　method　does　not　work　if　multiple　moving　objects　with　differe　the　time　of　measurement,　both　at　the　same　distance　from　the　radar.　Since　these　objects　are　at　the　will　generate　reflective　chirps　with　identical　IF　frequencies.　As　a　consequence,　the　range-FFT　will　re　which　represents　the　combined　signal　from　all　of　these　equi-range　objects.　A　simple　phase　compar　not　work.　毫米波雷达传感器基础知识　	　6	　2017　年5月(12)　使用位于同一距离处的多个物体进行的速度测量　如果速度不同的多个移动物体在测量时与雷达的距　离相同,则双线性调频脉冲速度测量方法不起作　用。这些物体由于与雷达的距离相同,因而会生成　IF　频率完全相同的反射线性调频脉冲。因此,距离　FFT　会产生单个峰值,该峰值表示来自所有这些距　离相同的物体的合并信号。简单的相位比较技术将　不起作用。　在这种情况下,为了测量速度,雷达系统必须发射　两个以上的线性调频脉冲。它发射一组　N　个等间隔　线性调频脉冲。这组线性调频脉冲称为线性调频脉　冲帧。图7显示了一个线性调频脉冲帧随时间变化　的频率。　下面以两个与雷达的距离相等但速度分别为　v1　和v2　的两个物体举例说明了处理技术。　距离　FFT　处理反射的一组线性调频脉冲,从而产　生一组　N　个位置完全相同的峰值,但每个峰值都有　一个不同的相位,包含来自这两个物体的相位成分　(来自各个物体的单独相位成分由图　8　中的红色和　蓝色相量表示)。　称为多普勒　FFT　的第二个　FFT　在N个相量上执　行,以分辨两个物体,如图　9　所示。　w1　和w2　对应于各个物体连续线性调频脉冲之间的　相位差(方程式　13):　(13)　速度分辨率　离散傅里叶变换的理论指出,两个离散频率　w1　和w2　在Dw　=　w2　–　w1　>　2p/N　个弧度/样本时,是可以　分辨的。　由于　Dw　也是由以下方程式　(方程式　10)　定义的,因而　当帧周期为(Vres)Tf　=　NTc(方程　式14),可通过数学方法推导出速度分辨率:　(14)　雷达的速度分辨率与帧时间　(Tf)　成反比。　角度检测　角度估算　FMCW　雷达系统可以使用水平面估算反射信号的角　度,如图　10　所示。该角度也称为到达角　(AoA)。　v1　v2　䴭䗴　ѱ㾷图8.反射线性调频脉冲帧的距离　FFT　会产生　N　个相量。　䴭䗴　⢟։　θ　图10.到达角。　c　T　1　2　3　N　图7.线性调频脉冲帧。　ω1　ω2　图9.多普勒　FFT　可区分这两个物体。　Figure　8.　The　range-FFT　of　the　reflected　chirp　frame　results　in　N　phasors.　A　second　FFT,　called　Doppler-FFT,　is　performed　on　the　N　phasors　to　resolve　the　two　objects,　as　shown　Figure　9.　Doppler-FFT　separates　the　two　objects.　ω1　and　ω2　correspond　to　the　phase　difference　between　consecutive　chirps　for　the　respective　objects　\ud835\udc63\ud835\udc631　=　\ud835\udf06\ud835\udf06\ud835\udf14\ud835\udf141　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　,　\ud835\udc63\ud835\udc632　=　\ud835\udf06\ud835\udf06\ud835\udf14\ud835\udf142　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(13)　Velocity　Resolution　You　have　already　seen　that　two　discrete　frequencies,　ω1　and　ω2,can　be　resolved　if　Δω=　ω2　-　ω1　>　2π/N　Since　Δω　is　also　defined　by　the　following　equation　∆\ud835\udf14\ud835\udf14　=　4\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　\ud835\udf06\ud835\udf06　(equation　10)　one　can　mathematicall　resolution(vres)　if　the　frame　period　Tf　=　NTc　(Equation　14):　Velocity　Measurement　In　this　section,　let’s　use　phasor　notation　(distance,　angle)　for　a　complex　number.　Velocity　Measurement　with　Two　Chirps　In　order　to　measure　velocity,　a　FMCW　radar　transmits　two　chirps　separated　by　Tc　Each　refle　through　FFT　to　detect　the　range　of　the　object　(range-FFT).　The　range-FFT　corresponding　to　the　same　location,　but　with　a　different　phase.　The　measured　phase　difference　corresponds　vTc.　Figure　6.　Two-chirp　velocity　measurement.　The　phase　difference　is　defined　as　Equation　10:　∆\ud835\udef7\ud835\udef7　=　4\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　\ud835\udf06\ud835\udf06　(10)　You　can　derive　the　velocity　using　Equation　11:　\ud835\udc63\ud835\udc63　=　\ud835\udf06\ud835\udf06Δ\ud835\udef7\ud835\udef7　4\ud835\udf0b\ud835\udf0b\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(11)　Since　the　velocity　measurement　is　based　on　a　phase　difference,　there　will　be　ambiguity.　Th　unambiguous　only　if　|∆\ud835\udef7\ud835\udef7|<　π.　Using　equation　11　above,　one　can　mathematically　derive　\ud835\udc63\ud835\udc63　Equation　12　provides　the　maximum　relative　speed　(vmax)　measured　by　two　chirps　spaced　Tc　shorter　transmission　times　between　chirps.　vmax　=　\ud835\udf06\ud835\udf06　4\ud835\udc47\ud835\udc47\ud835\udc50\ud835\udc50　(12)　Velocity　Measurement　with　Multiple　Objects　at　the　Same　Range　The　two-chirp　velocity　measurement　method　does　not　work　if　multiple　moving　objects　with　the　time　of　measurement,　both　at　the　same　distance　from　the　radar.　Since　these　objects　ar　will　generate　reflective　chirps　with　identical　IF　frequencies.　As　a　consequence,　the　range-FF　which　represents　the　combined　signal　from　all　of　these　equi-range　object