Practical information | Introduction to the basic principles of automotive millimeter wave radar

火辣西米秀

Practical information | Introduction to the basic principles of automotive millimeter wave radar [Copy link]

introduction

With the continuous pursuit of safe driving and intelligent transportation in modern society, automotive technology is developing towards unprecedented heights. Among them, millimeter-wave radar technology, as an advanced sensor technology, is leading a revolutionary change in the automotive field. With its high precision, reliability and adaptability, millimeter-wave radar plays an indispensable role in key areas such as autonomous driving, collision warning, and adaptive cruise control, pushing the safety, convenience and intelligence level of automobiles to a new level.

Radar in Car

1. Introduction

As a major sensing technology, millimeter wave radar plays an important role in automobile safety systems. It uses electromagnetic waves in the millimeter wave band to perceive the surrounding environment and detects and tracks other vehicles, pedestrians, obstacles, and road conditions by measuring the reflected signals.

Compared with traditional infrared sensors and lidar, millimeter wave radar has unique advantages. It can use electromagnetic waves in the millimeter wave frequency band to penetrate adverse weather conditions such as rain, snow and fog, thereby achieving reliable detection in complex environments.

This article will focus on the principles and working methods of automotive millimeter-wave radar. We will briefly explain the basic principles of millimeter-wave radar, including its operating frequency band and detection principle.

2. Introduction to FMCW radar

2.1 Basic Concepts

The millimeter-wave radars currently on the market are based on frequency-modulated continuous wave (FMCW) technology, so we will refer to millimeter-wave radars as FMCW radars below. As the name implies, FMCW radars continuously transmit frequency-modulated signals to measure distance, angle, and speed. FMCW radars use the phase and frequency of reflected signals to locate, measure speed, and so on, which is different from the principle of laser radars that periodically emit short pulses and then directly measure the return time. ( For more information about the principles of laser radars, please see another article on my official account, Detailed Explanation of the Basic Principles of Laser Radars )

The frequency of the signal used in FMCW radar systems increases linearly with time. This type of signal is also called a linear frequency modulated pulse. The figure below shows a linear frequency modulated pulse signal representation as a function of amplitude (amplitude) versus time (At).

FMCW tA Curve

With the vertical axis being frequency and the horizontal axis being time, the (ft) graph is shown below:

FMCW radar ft image

2.2 Basic Framework

The basic framework of FMCW radar is as follows:

FMCW radar basic architecture

It can be seen that FMCW radar consists of the following basic components:

• Transmitting Antenna (Tx Antenna) & Receiving Antenna (Rx Antenna)
• Mixer
• Clock source (crystal oscillator)
• ADC & DSP

2.3 Workflow

The radar workflow is as follows:

• The synthesizer generates a linear frequency modulated pulse;
• This chirp is transmitted by the transmit antenna (TX antenna);
• The reflection of this chirp by the object generates a reflected chirp that is captured by the receiving antenna (RX antenna);
• The “mixer” combines the RX and TX signals to create an intermediate frequency (IF) signal.

in:

A mixer is an electronic component that combines two signals to create a new signal with a new frequency.

The explanation is as follows:

For two sinusoidal function signals X1 and X2:

The instantaneous frequency of the output Xout is equal to the difference between the instantaneous frequencies of the two input sine functions. The phase of the output is equal to the difference between the phases of the two input signals, as follows:

3. Distance measurement principle

3.1 Radar Signal

Taking single object detection as an example, the representation of Tx, Rx and mixed IF signals using time-to-frequency (ft) images is shown below:

FMCW ranging principle signal image

Output input frequency image

It can be seen that the mixing signal IF is a sinusoidal signal with a fixed frequency:

3.2 Distance Calculation

Assuming the distance of the object is d, the delay τ between Rx and Tx is calculated as follows:

Where: d is the distance, c is the speed of light

Note: d is the distance to the object to be measured, and τ is the flight time of the electromagnetic wave. Since the flight time is extremely short, it is very costly to directly measure τ using hardware (refer to lidar).

So: Here is another way. We use FFT to infer the frequency and phase of the signal, and convert it to obtain information such as speed and distance. The derivation process is as follows:

We learned in high school that the relationship between angular frequency and frequency is as follows:

Then the initial phase of the IF signal obtained by mixing Rx and Tx is:

Where: fc is the initial frequency of the radar's Tx signal

because:

therefore:

Where λ is the initial signal wavelength (c=fλ)

Secondly, according to the FMCW ranging principle image, we can know that the frequency fo of the mixed IF signal is:

Where: S is the FMCW frequency change rate, in Mhz/s

Then, the IF signal can be expressed as follows:

Including:

At this point, we know that for a reflecting object, we can do FFT on the IF signal to know its frequency f and phase φ, so its distance is:

Generally we use frequency calculation.

3.3 Multi-target distance calculation

For multi-target objects, the IF mixed signal has different distances from multiple reflection targets, so the reflected image is as follows:

Multiple target reflection signals

It can be seen that multiple target reflections correspond to multiple Rx signals, and their frequencies and phases are different. After performing FFT on the IF signal, multiple trunk frequencies can be obtained as follows:

Multi-objective FFT

pass:

Then we can calculate the distances of these three objects respectively.

3.4 Distance Resolution Calculation

Range resolution is the ability to distinguish between two or more objects. When two objects are close to a certain position, the radar system will no longer be able to distinguish between the two objects. Fourier transform theory shows that by extending the IF signal, the resolution can be improved.

But to stretch the IF signal, the bandwidth must also be increased proportionally. The stretched IF signal produces an IF spectrum with two separated peaks.

Fourier transform theory also states that the observation window (T) can resolve frequency components with a spacing greater than 1/THz. This means that two IF single-tone signals can be resolved as long as the frequency difference satisfies the relationship given in the following formula.

Among them, Tc is the observation time length, that is, the time length of the FFT signal.

And because:

therefore:

The distance resolution is therefore:

Therefore, for an FMCW radar with a bandwidth of GHz, the resolution is approximately at the cm level. For example, for a radar with a bandwidth of B=4Ghz, the distance resolution is 3.75cm.

Now that the distance has been calculated, how are the speed and angle calculated? Please continue reading!!!

4. Speed measurement principle

4.1 Radar speed measurement signal

To measure velocity, the FMCW radar transmits two chirps separated by a distance Tc. Each reflected chirp is processed by an FFT, called a range FFT, to detect the distance to the object. The range FFT corresponding to each chirp will have a peak at the same location, but with a different phase. This measured phase difference corresponds to the movement of an object with a velocity vTc.

Dual linear pulse velocity measurement

From the phase difference formula we can know:

So we have:

Since the velocity measurement is based on the phase difference, there is an ambiguity or periodicity because the phase is periodic (-π, π). This measurement is unambiguous only when |Δφ| < π.

Therefore, when |Δφ| = π, the maximum measurable speed of the radar is:

4.2 Speed Calculation of Different Objects at the Same Location

The dual chirp velocity measurement method does not work if multiple moving objects with different speeds are measured at the same distance from the radar. These objects, being at the same distance from the radar, will generate reflected chirps with exactly the same IF frequency. Therefore, the range FFT will produce a single peak representing the combined signal from all these objects at the same distance. Simple phase comparison techniques will not work.

In this case, to measure the velocity, the radar system must transmit more than two chirps. It transmits a group of N equally spaced chirps. This group of chirps is called a chirp frame.

The following graph shows the frequency of a chirp frame varying over time:

Chirp

The range FFT processes the reflected set of chirps to produce a set of N peaks at exactly the same locations, but each with a different phase containing phase contributions from both objects (the separate phase contributions from each object are represented by the red and blue phasors in the figure below).

N vectors generated by the distance FFT

Here, v1 and v2 can be obtained through Doppler FFT, that is, FFT is performed on each signal of n groups of signals separately. For details, please refer to the following figure:

Doppler FFT

Through Doppler FFT, two objects with different speeds can be distinguished:

Doppler FFT to differentiate between two objects

Where w1 and w2 correspond to the phase difference between the continuous linear frequency modulation pulses of each object, the speed of the two objects can be obtained as follows:

4.3 Velocity resolution

The theory of the discrete Fourier transform states that two discrete frequencies w1 and w2 are resolvable if Δw = w_2 – w1 > 2π / N radians/sample.

therefore:

5 Angle measurement

5.1 Angle measurement conditions

FMCW radar systems can use the horizontal plane to estimate the angle of the reflected signal, also known as the angle of arrival (AoA), as shown in the following figure:

Radar Angle of Arrival

It should be noted that radar angle estimation requires at least two Rx antennas, as shown in the following figure:

Angle estimation using 2Rx antenna

5.2 Angle measurement derivation

We know that for the same object, the phase difference received by the two receiving antennas is:

in:

therefore:

Therefore, the angle can be obtained by inverse trigonometric function:

Note that Δφ depends on sin(θ), which is called a nonlinear dependence.

AoA Accuracy

Similar to the speed calculation method, if you want to calculate the angle deviation of the object, you need to calculate the phase difference between different receiving antennas. Here comes the third angle FFT. The reference image is as follows:

Doppler FFT

5.3 Maximum field of view

The maximum angular field of view of a radar is defined by the maximum AoA that the radar can estimate, as follows:

Maximum AoA

Since the precise measurement of angles is limited to |Δw| < 180°, the corresponding relationship is:

Therefore, the maximum angle is:

It can be seen that the spacing d = λ/2 between the two antennas will result in a maximum angular field of view of ±90°.

6. Summary and Results

Radars of different frequencies have different measurement distances and maximum detection angles. Currently, the most basic algorithm for Radar is FFT, which obtains the motion information of an object based on distance FFT, velocity FFT, and angle FFT, and finally obtains a radar image.

The typical effect of Radar is as follows:

Measuring the effect

It can be seen that the current 3D Radar detection effect is a plane data, which only has speed v, distance d and angle θ information, but lacks height h information. This will be optimized in the subsequent 4D Radar, which we will talk about later.

references

[1] Basic knowledge of millimeter wave radar sensors

[2] MIMO Radar

chejm

The technical knowledge shared by the host is very detailed, with pictures and texts, and the content is easy to understand. I benefited a lot. Thank you for the host

lugl4313820

Currently, the most basic algorithm of Radar is FFT, which obtains the motion information of the object based on distance FFT, speed FFT and angle FFT, and finally obtains the radar image.

It seems that learning FFT is very necessary!