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힌트: 여러 단어는 쉼표로 구분
Date
예: 06/24/2022
Date
예: 06/24/2022
Global
China (简体中文)
Japan (日本語)
Korea (한국어)
Taiwan (繁體中文)
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Comparison of 3D ToF and mmWave for robot vision
Comparison of 3D ToF and mmWave for Robot Vision (Part 2)
Comparison of 3D ToF and mmWave for robot vision
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Comparison of 3D ToF and mmWave for Robot Vision (Part 2)
Hello, everyone. This is Richard Wang from Industrial System team of Texas Instruments. Welcome to Part 2 of the training series on comparison of the 3D time of flight and mmWave for Robot Vision applications. In this part, we will have a brief introduction of mmWave and learn how mmWave readers sense the range, velocity, and angle. Then there will be overview instruction of the TI radar devices and tools. MmWave, also called millimeter wave, it means magnetic waves from 1 to 10 millimeters. Then in a frequency spectrum experienced 30 to 300 giga Hertz. It travels in speed of light and obeys the laws of geometrical optics. A frequency modulated continuous wave radar, also called FMCW radar, transmit a signal called a chirp. A chirp is a sinusoidal signal who's frequency increased linearly with time, as shown in this amplitude versus time, or A-t plot here. A frequency versus time plot, or f-t plot, is a convenient way to represent a chirp. A chirp is characterized by our start of frequency, fc, bandwidth, B, and duration, Tc. The Slope, S, of the chirp defines the rate at which the chirp ramps up. In this example, the chirp is sweeping a bandwidth of four gigahertz in 40 micro-seconds, which corresponds to a Slope of 100 megahertz per micro-second. Here, you have a simplified plot diagram of a FMCW radar with a single TX and a single RX antenna. The radar operates as follows. The synthesizer generates a chirp. This chirp is transmitted by the TX antenna. The chirp is reflected off an object and the reflected chirp is received at the RX antenna. The RX signal and TX signal are 'mixed' and the resulting signal is called an 'IF signal'. IF standing for intermediary frequency. Then what is a mixer? A mixer is a three port device with two inputs and one output. For our purposes, a mixer can be modeled as follows. For two sinusoids x1 and x2, input at the two input ports, the output is sinusoidal with instantaneous frequency equal to the difference of the instantaneous frequencies of the two input sinusoids, phase equal to the difference of the phase of the two input sinusoids. The mixer operation can be understood easily using a f-t plot. So the plot here refers to the RF signal. So you have the transmitter chirp here in AT plot and here in f-t plot. After reflection, the receiver chirp is shown here in AT plot and here in f-t plot. Note that the receiver chirp is a time-delayed replica of the TX chirp. And for now, I'm assuming there is only one object in front of the radar hence, only one RX chirp. Remember from the last slide that output frequency of the mixer uses the difference of the instantaneous frequencies its two inputs, namely the TX chirp and the RX chirp. So to generate the f-t plot of the IF signal, I just need to subtract this line from this. And as you can see, these two lines are at a fixed distance from each other and that fixed distance is given by the Slope of the chirp times the round trip delay, in other words, S tau. So a single object in front of a radar produces a IF signal consisting of a single frequency given by S tau. Now, tau, the round trip delay from the radar to the object and back can also be expressed as twice the distance to the object divided by the speed of light. So this is a fundamental concept to remember. A single object in front of a radar produces a IF signal with a constant frequency given by S2d divided by c. It's easy to extend this to the case where there are multiple objects in front of a radar. So here, you have a radar transmitting a single chirp. And you can get mulitple reflected chirps from different objects each delayed by a different amount depending on the distance to that object. So the IF signal will have the tones corresponding to each of these reflections. And the frequency of these tones, as we learned, is directly proportional to range. So this have the smallest frequency and it corresponds to the closest object, while this corresponds to the farthest. A frequency spectry of this IF signal will then show multiple peaks. And the frequency of these peaks will be directly proportional to the range of the corresponding object. So again, this corresponds to the closest object and this one to the farthest. This slide summarizes all that we have discussed so far. This is a plot diagram of a FMCW radar with a single transmit and a single receiver antenna. Let's go with a sequence of events involved in estimating the range of the object. So first, the synthesizer, or synth, generates a chirp. This chirp is transmitted over the TX antenna and is reflected off multiple objects in front of the radar. And the receiver sees a delayed version of this chirp. The received signal and the transmitted signal are mixed to create a IF signal. This IF signal consists of multiple tones and the frequency of each of these tones is proportional to the range of the corresponding object. The IF signal is then low pass filtered and digitized. And note that the sampling rate of ADC must be commensurate with the maximum distance that we wish to see. The digitized data is then processed. Now, FFT is performed on this data and the location of the peaks in the frequency spectrum directly correspond to the range of the objects. Note that here, I plot the FFT with range on the x-axis rather than IF's frequency, which is OK. But as we have learned, the IF frequency is directly proportional to range. This FFT is called a 'range-FFT' because the result [INAUDIBLE] in a range. And this term, 'range-FFT', is something that you will see a lot in FMCW literature. Here lists some key parameters for range. The frequency of IF signal equals Slope of chirps times 2d divided by the speed of light. The range resolution depends on bandwidth as shown in this equation. The ADC sampling rate limits the maximum range d max that a radar can see. The typical number for range resolution is shown here. One bandwidth is four gigahertz. The range resolution is 3.75 centimeters. Next, we will learn how the radar senses the velocity. Before that, let's check the phase of IF signal. Here, it shows the A-t plot for TX chirp. The one in the middle is RX chirp, which is just a delayed version of the TX chirp, delayed by moment of tau, tau being the round trip delay. For a single object the IF signal is going to be a constant frequency signal, in other words, a single sinusoid. So mathematically, I can represent this IF signal with Asin 2 pi times f-t plus phi 0, where f, the frequency, is given by S2d divided by c, S being the slope, d being the distance to the object, and c, the speed of light. And phase of phi 0 is just in a phase of this IF signal at a point of c. We know that the initial phase of IF signal at mixer output is the difference of the initial phases of the two inputs. So this phase at c is going to be the difference of phase of the TX chirp at point of A and at the phase of RX chirp at point B. So if the object moves by a small amount of new IF signal represented by the blue curve here, it's going to shift by an amount of delta tau. Also, the IF signal is correspondingly going to be changed. Now, the starting phase of the new IF signal at a point of f is going to be the difference of phase D and phase E. Now, the phase of the RX chirp at E is going to be the same with the phase of earlier IF signal at B. But the phase of the TX chirp at D is going to be the earlier phase at A with the additional phase offset of 2 pi fc delta tau. And this is because the TX chirp would have traversed an additional phase of the 2 pi fc delta tau during this period, delta tau. And this additional phase which is the phase difference between the point A and D is going to get [INAUDIBLE] in the phase of IF signal, that is, the phase at F. So the change in the phase of IF signal when an object moves by delta tau is a given by delta phi equals 2 pi fc delta tau, which I can also rewrite in terms of the corresponding change in distance to the object, delta d is 2 pi delta d divided by lambda where I have used the fact that the delta tau is equal to twice the change in a distance divided by the speed of light. And the wavelength is equal to the speed of light divided by the frequency fc. For object at a distance D from the radar the IF signal is a sinusoid with a frequency F given by this equation here in a phase which linearly responds to small change delta d in the distance to the object. Based on analysis before, you know the measure of velocity of an object. The radar transmit two chirps separated by Tc. Because of a small distance change delta d the reflection range-FFT is corresponding to each chirp. We'll have peaks in the same location but with differing phase. Assume that an object moves at a speed of v given a Tc then if delta d equals vTC, we can get this formula. So the phase difference measured across two consecutive chirps can be used to estimate the velocity of an object. What about multiple objects? Use this example. Two objects in front of a radar with the same range from radar but have different velocities, V1 and V2, relative to the radar. Phasor at the peak is going to have the components for both objects. The radar needs to resolve these two objects and figure out the phase difference for both. In order to do that, radar will transmit a series of equi-spaced chirps instead of just two chirps, which is shown here. This unit is typically called a frame. An FFT on the sequence of the phasors, which is called doppler-FFT resolves the two objects by two peaks, which are shown here. Here are some parameters for velocity. The velocity resolution of the radar is inversely proportional to the frame time Tf and it's given by this formula. This formula shows the maximum relative speed, Vmax, that can be measured by two chirps spaced Tc apart. The next the question is how the radar senses the angle of an object. The angle estimation for radar is based on the antenna array for one object. Angle estimation requires at least two RX antennas. We still remember that a small change in the distance of the object-- now, for example, delta d-- result in a phase change, omega here, in the peak of the range-FFT. Similarly, the differential distance from the object to each of the antennas is delta d and results in a phase change in the 2D-FFT peak, which is exploited to estimate the angle of arrival. Assume D is the distance between two antennas and theta is the angle of arrival of that object with respect to the radar. By using geometry, the additional distance for object to the second antenna compared to the first antenna is d sin theta. So the transmitter antenna transmit a frame of chirps and the data is received in each of these antennas. And each of these antenna processes the data to create a 2D-FFT matrix with a peak corresponding to range and velocity of the object. So here, you have the 2D-FFT peaks corresponding to this antenna and another 2D-FFT matix corresponding to this antenna. Note that the location of the peak is going to be virtually identical for both of these 2D-FFTs. The phase difference between these two peaks is going to be given by 2 pi dsin theta. dsin theta being the additional distance divided by Lambda. And once you have measured this phase difference by comparing these two signals, the signal on these two peaks you can just invert this equation to calculate an angle of arrival. If there are two or more objects in front radar at the same range and same relative velocity with respect to radar, then both objects for give the same range velocity being in a 2D-FFT. So this is the 2D-FFT from the first antenna and this is the 2D-FFT from the second antenna. So there is a single peak in this 2D-FFT, but the signal at a peak will have contributions from phasors corresponding to both of these objects. It's going to be a very analogous to what we did earlier with the module on velocity. We increased the number of RX antenna from 2 and create an area of N antennas. N receive antennas and the two dimensional FFT at all these antennas is going to have a peak at the same location. And the signal at this series of peaks is going to create a discrete sequence consisting of two rotating phases as shown here. And f of d on the sequence we are show up as two peaks, and omega 1 and omega 2, where omega 1 and omega 2 are the rates of the rotation in radiance per sample for the two objects. So you've written an equation of these two peaks from the FFT and then just back calculate the angle of arrivals for the two objects, as shown here. We call this particular FFT here, which is a performed across RX antennas as the angle-FFT. This is a comparison of angle and velocity estimation. We use antenna array to estimate the angle amount for objects and they use chirp frame to estimate the velocity of multiple objects. TI offers two chip set for you to choose. IWR1443 is an Entry-level Single-chip sensor, which is used for power optimized applications. The integrated hardware acceleration for limited processing. The IWR1642 is the advanced Single-chip rada with full functionality. It has increased on-board memory and on-chip DSP can be used for advanced algorithms. Here it shows the signal processing of TI mmWave radar. After three times of FFT, the radar can get the range, velocity, and angle of objects. TI takes pride in delivering the complete products to customers through [INAUDIBLE] software, tools, training, online support, and a vast ecosystem of partners. You can visit the following link to find them and the [INAUDIBLE] design. Thanks for watching.
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