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This example shows how model of an automotive radar in Simulink for an adaptive cruise control (ACC) system, which is an important part of an advanced driver assistance system (ADAS). The example explores both single and multiple targets scenarios. It shows how FMCW and MFSK waveforms can be processed to estimate the range and speed of surrounding vehicles.

**Available Example Implementations**

This example includes four Simulink® models:

FMCW Radar Range Estimation: slexFMCWExample.slx

FMCW Radar Multiple Targets Range and Speed Estimation: slexFMCWMultiTargetsExample.slx

Multiple Targets Range and Speed Estimation Using MFSK: slexMFSKMultiTargetsExample.slx

FMCW Radar Multiple Targets Range, Speed, and Angle Estimation: slexFMCWMultiTargetsDOAExample.slx

The following model shows an end-to-end FMCW radar system. The system setup is similar to the MATLAB Automotive Adaptive Cruise Control Using FMCW Technology example. The only difference is in this model the FMCW waveform sweep is symmetric around the carrier frequency.

The figure shows the signal flow in the model. The Simulink blocks which make up the model are divided into two major sections, the **Radar** section and the **Channel and Target** section. The shaded block on the left represents the radar system. In this section, the FMCW signal is generated and transmitted. This section also contains the receiver which captures the radar echo and performs a series of operations, such as dechirp and pulse integration, to estimate the target range. The shade block on the right models the propagation of the signal through space and its reflection from the car. The output of the system, the estimated range in meters is shown in the display block on the left.

**Radar**

The radar system consists of a co-located transmitter and a receiver mounted on a vehicle moving along a straight road. It contains the signal processing components needed to extract the information from the returned target echo.

`FMCW`

- Create FMCW signal. The FMCW waveform is a common choice in automotive radar because it provides a way to estimate the range using a continuous wave radar. The distance is proportional to the frequency offset between the transmitted signal and received echo. The signal sweeps a bandwidth of 150 MHz, which translates to a 1-meter resolution.`Transmitter`

- Transmits the waveform. The operating frequency of the transmitter is 77 GHz.`Receiver Preamp`

- Receives the target echo and adds the receiver noise.`Radar Platform`

- Simulates radar vehicle trajectory.`Signal Processing`

- Processes the received signal and derives the range of the target vehicle.

Within the **Radar**, the target echo goes through several signal processing steps in order to derive the target range. The signal processing subsystem, shown in more detail below, consists of three blocks. The first block dechirps the received signal by multiplying it with the transmitted signal. This operation produces a beat frequency between the target echo and the transmitted signal. The target range is proportional to the beat frequency. This operation also reduces the bandwidth required to process the signal. The second block sends the dechirped pulses through a pulse integrator to boost the signal-to-noise ratio (SNR). The third block, the Range Estimator, generates a periodogram, from which the peak is located to obtain the beat frequency. Estimating range becomes essentially a spectral analysis problem.

**Channel and Target**

The **Channel and Target** part of the model simulates the signal propagation and reflection off the target vehicle.

`Channel`

- Simulates the signal propagation between the radar vehicle and the target vehicle. The channel can be set as either a line of sight free space channel, or a two-ray channel where the signal arrives at the receiver via both the direct path and the reflected path off the ground. The default choice is a free space channel.

`Car`

- Reflects the incident signal and simulates the target vehicle trajectory. The subsystem, shown below, consist of two parts: a target model to simulate the echo and a platform model to simulate the dynamics of the target vehicle.

In the Car subsystem, the target vehicle is modeled as a point target with a specified radar cross section. The radar cross section is used to measure how much power can be reflected from a target.

In this model's scenario, the radar vehicle starts at the origin, traveling at 100 km/h (27.78 m/s), while the target vehicle starts at 50 meters in front of the radar vehicle, traveling at 96 km/h (26.67 m/s). The positions and velocities of both the radar and the target vehicles are used in the propagation channel to calculate the delay, Doppler, and signal loss.

**Exploring the Model**

Several dialog parameters of the model are calculated by the helper function helperslexFMCWParam. To open the function from the model, click on `Modify Simulation Parameters`

block. This function is executed once when the model is loaded. It exports to the workspace a structure whose fields are referenced by the dialogs. To modify any parameters, either change the values in the structure at the command prompt or edit the helper function and rerun it to update the parameter structure.

**Results and Displays**

The spectrogram of the FMCW signal below shows that the signal linearly sweeps a span of 150 MHz approximately every 7 microseconds. This waveform provides a resolution of approximately 1 meter.

The spectrum of the dechirped signal is shown below. The figure indicates that the beat frequency introduced by the target is approximately 100 kHz. Note that after dechirp, the signal has only a single frequency component. The resulting range estimate calculated from this beat frequency, as displayed in the model, is 49.95 meters, which is within the range resolution.

However, this result is obtained with the free space propagation channel. In reality, the propagation between vehicles often involves multiple paths between the transmitter and the receiver. Therefore, signals from different paths may add either constructively or destructively at the receiver. The following section set the propagation to a two-ray channel, which is the simplest multipath channel.

Run the simulation and observe the spectrum of the dechirped signal.

Note that there is no longer a dominant beat frequency because at this range, the signal from the direct path and the reflected path cancels each other out. This can also be seen from the estimated range. which no longer matches the ground truth.

The example model below shows a similar end-to-end FMCW radar system working with two targets. This example also estimates the speed of both target vehicles.

The model is essentially the same as the previous example with two differences. Besides having two targets, the radar system now uses range-Doppler joint processing.

**Radar**

This model uses range Doppler joint processing in the signal processing subsystem. Joint processing in range-Doppler domain makes it possible to estimate the Doppler across multiple sweeps and then to use that information to resolve the range-Doppler coupling, resulting in better range estimates.

The signal processing subsystem is shown in detail below.

The blocks that make up the signal processing subsystem are

`Dechirp`

- Dechirps the received signal.`Pulse Buffer`

- Buffers the incoming signal to form a fast time vs. slow time matrix.`Range Doppler Response`

- Computes the range-Doppler map based on the signal matrix.`Up Sweep Range Speed Estimation`

- Estimates the range and speed of the targets from the range-Doppler map.

Once the signal is dechirped, it is buffered to form a matrix and then processed to generate the corresponding range-Doppler map. The next step analyzes the map and derives the range and speed of the targets. The details of the range and speed estimation are shown below.

`Range Estimator`

- Estimates the target range from the range-Doppler map.`Speed Estimator`

- Estimates the target speed from the range-Doppler map based on the range estimates.`Range Doppler Decoupler`

- Removes the range estimation error due to range-Doppler coupling.

As mentioned in the beginning of the example, FMCW radar uses a frequency shift to derive the range of the target. However, the motion of the target can also introduce a frequency shift due to the Doppler effect. Therefore, the beat frequency has both range and speed information coupled. Processing range and Doppler at the same time lets us remove this ambiguity. As long as the sweep is fast enough so that the target remains in the same range gate for several sweeps, the Doppler can be calculated across multiple sweeps and then be used to correct the initial range estimates.

**Channel and Target**

There are now two target vehicles in the scene, labeled as Car and Truck, and each vehicle has an associated propagation channel. The Car starts 50 meters in front of the radar vehicle and travels at a speed of 60 km/h (16.67 m/s). the Truck starts at 150 meters in front of the radar vehicle and travels at a speed of 130 km/h (36.11 m/s).

**Exploring the Model**

Several dialog parameters of the model are calculated by the helper function helperslexFMCWMultiTargetsParam. To open the function from the model, click on `Modify Simulation Parameters`

block. This function is executed once when the model is loaded. It exports to the workspace a structure whose fields are referenced by the dialogs. To modify any parameters, either change the values in the structure at the command prompt or edit the helper function and rerun it to update the parameter structure.

**Results and Displays**

The FMCW signal shown below is the same as in the previous model.

The two targets can be visualized in the range-Doppler map below.

The map correctly shows two targets: one at 50 meters and one at 150 meters. Because the radar can only measure the relative speed, the correct estimates of speeds for these two vehicles are 11.11 m/s and -8.3 m/s, respectively, where the negative sign indicates that the Truck is moving away from the radar vehicle. The exact speed estimates may be difficult to read out from the map, but the estimated ranges and speeds are shown in the display blocks in the block diagram. From the displayed results, the speed estimates are also correct.

To be able to do joint range and speed estimation using the above approach, the sweep needs to be fairly fast to ensure the vehicle is approximately stationary during the sweep. This often translates to higher hardware cost. MFSK is a new waveform designed specifically for automotive radar so that it can achieve simultaneous range and speed estimation with longer sweeps.

The example below shows how to use MFSK waveform to perform the range and speed estimation. The scene setup is the same as the previous model.

The only differences are in the waveform block and the signal processing subsystem. The details of MFSK waveform is described in the Simultaneous Range and Speed Estimation Using MFSK Waveform example but it essentially consists of two FMCW sweeps with a fixed frequency offset. The sweep also happens at discrete steps. From the parameters of the MFSK waveform block, the sweep time can be computed as the product of the step time and the number of steps per sweep. In this example, the sweep time is slightly over 2 ms, which is several orders larger than the 7 microseconds for the FMCW used in the previous model.

The signal processing subsystem describes how the signal gets processed for the MFSK waveform. The signal is first sampled at the end of each step and then converted to frequency domain via FFT. A CFAR detector is used to identify the peaks, which correspond to targets, in the spectrum. Then the frequency at each peak location as well as the phase difference between the two sweeps are used to estimate the range and speed of target vehicles.

**Exploring the Model**

Several dialog parameters of the model are calculated by the helper function helperslexMFSKMultiTargetsParam. To open the function from the model, click on `Modify Simulation Parameters`

block. This function is executed once when the model is loaded. It exports to the workspace a structure whose fields are referenced by the dialogs. To modify any parameters, either change the values in the structure at the command prompt or edit the helper function and rerun it to update the parameter structure.

**Results and Displays**

The estimated result is shown in the model, matching the result obtained from the previous model.

One can improve the angular resolution of the radar by using an array of antennas. This example shows how to resolve three target vehicles traveling in separate lanes ahead of a vehicle carrying an antenna array.

In this scenario, the radar is traveling in the center lane of a highway at 65 mph. The first target vehicle is traveling 20 meters ahead in the same lane as the radar at 55 mph. The second target vehicle is traveling at 80 mph in the right lane and is 40 meters ahead. The third target vehicle is traveling at 70 mph in the left lane and is 80 meters ahead. The antenna array of the radar vehicle is a 4-element ULA.

Fix the origin of the coordinate system at the radar vehicle, the ground truth range, speed, and angle of the target vehicles with respect to the radar is

Range (m) Speed (m/s) Angle (deg) --------------------------------------------------------------- Car 1 20 4.44 0 Car 2 40.05 -6.66 -2.86 Car 3 80.03 -2.22 1.43

The signal processing subsystem now includes direction of arrival estimation in addition to the range and Doppler processing units.

As shown in the diagram, the first step in the signal processing chain is range estimation. Once the range a target is estimated, the data in the corresponding range bins are used to estimate the speed (range rate) and the direction of arrival of the same target.

**Exploring the Model**

Several dialog parameters of the model are calculated by the helper function helperslexFMCWMultiTargetsDOAParam. To open the function from the model, click on `Modify Simulation Parameters`

block. This function is executed once when the model is loaded. It exports to the workspace a structure whose fields are referenced by the dialogs. To modify any parameters, either change the values in the structure at the command prompt or edit the helper function and rerun it to update the parameter structure.

**Results and Displays**

The estimated result is shown in the model. The range estimates are within 0.5 meter; the speed estimates are within 0.1 m/s; and the angle estimates are within 0.1 degrees. Therefore, the estimates matching the ground truth well.

The first model shows how to use an FMCW radar to estimate the range of a target vehicle. The information derived from the echo, such as the distance to the target vehicle, are necessary inputs to a complete automotive ACC system.

The example also discusses how to perform range Doppler processing to derive both range and speed information of target vehicles. However, it is worth noting that when the sweep time is long, the system capability for estimating the speed is degraded and it is possible that the joint processing can no longer provide accurate compensation for range Doppler coupling. More discussion on this topic can be found in the MATLAB Automotive Adaptive Cruise Control Using FMCW Technology example.

Next model shows how to perform the same range and speed estimation using MFSK waveform instead. This waveform can achieve the joint range and speed estimation with longer sweeps, thus reducing the hardware requirements.

The last model shows uses FMCW waveform again and shows how to perform the range, speed, and angle estimation simultaneously if an antenna array is available in the radar system.

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