Rebirth -- millimeter wave radar and some things I have to say

1 , FMCW Basic concepts

FMCW At the heart of this is a system called Linear frequency modulation pulse （chrip） The signal of . LFM pulse refers to the pulse of radar signal frequency Over time Linear growth Of Sine wave （f=at）, Time domain waveform See figure above  

  Suppose that the LFM pulse is at a frequency of fc Start , When time Tc In the past 40us after , With a final fc +B The frequency of （ Echo received ）, that B For linear frequency modulation pulse bandwidth . So we call it frequency modulated continuous wave , namely FMCW. The picture above shows FMCW Frequency domain waveform ： among B and S Will be an important parameter

2 , FMCW working principle

2.1 Mixer knowledge

  Workflow ： The emitter （ Synthesizer ） produce   Linear frequency modulation signal adopt TX Transmit antenna Signal , After touching an object , The signal bounces off RX Receiving antenna , also adopt Mixers mixer hold Received signal and LFM signal at this time blend , obtain IF If signal

             

     How the mixer works

2.2 If signal IF

Now let's take a look outside. Suppose there is only one object in front of the radar ,IF How to obtain if signal , That is, what the final output signal is .

  By the previous Mixers The working principle is known ,IF The signal From two sinusoidal signals frequency , phase , respectively, Do a bad job . So here we also use Send frequency subtract Receiving frequency .（w and f It's just bad 2Π Relationship ：w=2Πf, So it doesn't affect ）

Now? , Let's analyze the lower part of the above figure .t It can be used distance / The speed of light Of 2 Multiple representation （ Because the object was hit by radar and returned to the same d）. namely 2d/c=t（ Because distance / Speed = Time ）. According to the vertical coordinate of the figure ：St = f（f by IF The frequency of ）, therefore f=2dS/c

matters needing attention ：IF The signal must be in time t after , That is to say, the radar generates the echo after receiving it , And IF The duration of the signal time is also limited , let me put it another way , You must process the signal within the specified time

2.3 The Fourier transform

The Fourier transform ： Reflect the signal from time domain to frequency domain

  The above is the basic Fourier transform formula , But we mainly start from Figure to understand , A sine wave in the frequency domain . Let's add , The reason why frequency domain observation is used is that frequency domain is important for f Very sensitive , The distribution of different frequencies can be well observed

  This is the frequency domain conversion diagram of a sine wave ！ Now let's add the sine wave , What will happen ？

answer ： Two cases ！

Case one ： Can't tell ！ Because if the frequencies of the two signals are close , That is to say, in the time domain, the two pass through the same time , But after different cycles ！ Here is the difference Half a cycle .

  The second case ： Can distinguish . The same signal , But the observation time increases , This will cause the last two signals to differ in time domain A cycle , Then two peaks will be resolved in the frequency domain

summary ： Observation window time T higher than T Frequency classification separated by 1/hz , in other words Longer observation , The better the result. , But we It is impossible to increase the observation time infinitely ！

Add ： Actually, increase the observation time , Is it equivalent to increasing the bandwidth of the signal ？

2.4 Multi object detection

It has been analyzed above that if there are two signals , Now let's assume that there are multiple objects in front of the radar , Let's analyze the multiple objects at this time IF Signal situation ！

 

As you can see from the picture above , If there are many objects , Then it will receive more echoes , Then according to the single echo principle , Is it possible to get multiple IF The signal . And it's easy to know ,IF The lower the frequency of the signal , So the object is closer .

Then there will be multiple peaks in the frequency domain , And according to the above frequency and distance properties , You can also see who is far or near from the frequency domain diagram .

2.5 Range resolution

The essence ： When the detected object is very close , So how can we tell two objects ！

terms of settlement 1： Increase the observation time , you 're right , As mentioned above, this is a method ！ Now let's continue to deduce ！

We have already got these three formulas ：        

Now deform the three formulas as shown in the figure below ：

  So I want to distinguish two objects , Then the distance between these two objects satisfies the above The speed of light /2 Double bandwidth

2.6IF signal processing

We know , Got IF Signals often need to be processed , The general flow here is as follows ：

  Then for subsequent processing , Let's analyze the following situation again ：

The question is who has the better resolution ？

I guess it must be A, Because I said before , The longer you observe , Then the effect is better . Yes, of course , We know from the resolution formula that these two should be the same ！ What are the facts ？ Let's move on ！

---

Said just now ,IF The signal still needs to be processed, right , Then when passing through the low-pass filter , Whether the cut-off frequency of the filter should be greater than IF The frequency of , Because it is not greater than this frequency , The signal will be lost ！

---

Out of class , stay ADC part , The sampling rate here should also be greater than IF frequency , therefore ADC The maximum sampling rate will limit the maximum range of the radar

---

So we can know from the following formula ： We prefer to use signals with smaller slopes , Because for the same distance , The slope is small , The sampling rate is small , The hardware requirements are much better

 2.7 RF bandwidth and IF bandwidth

RF bandwidth ：

The essence ： The bandwidth that LFM pulses span

characteristic ：（1） The larger the size, the better the range resolution

           （2）4Ghz Can have 4cm The resolution of the

IF bandwidth

The essence ： Namely IF The maximum frequency is less than the minimum frequency difference

characteristic ：（1） The larger it is, the farther it can be detected

           （2） Achieve a higher slope FMCW

---

---

It's over here ！ Goodbye in the Jianghu ！