Frequency Modulation Continuous wave (FMCW) is a leading technology in the field of optical LiDAR. FMCW LiDAR offers several advantages, such as improved range resolution, better dynamic range, and the ability to measure both speed and distance simultaneously. In this example, we will demonstrate a LiDAR system using INTERCONNECT, incorporating a FMCW laser source with homodyne detection to measure both distance and speed of a moving object.
Overview
Understand the simulation workflow and key results
In this example, we decompose the simulation into three steps:
Step 1: Setting up the FMCW Laser
The main purpose of this step is to ensure the FMCW laser source is set up correctly. This involves configuring the laser to emit a chirped signal, which is essential for accurate distance and speed measurements. In addition, the environment parameter "time window" is set to configure FMCW laser correctly. Detail discussion could be found in important model settings. (Sampling rate and df).
Step 2: System simulation
In this step, we first estimate the phase change due to Doppler shift. Then we simulate a LiDAR system, incorporating the FMCW laser source, this Doppler shift and traveling phase. The speed and distance could therefore be calculated based on the theory mentioned in the appendix. In addition, details about Doppler shift calculation could be found in important model settings. (Phase change due to Doppler shift).
Step 3: Deviation due to nonlinear frequency modulation sensitivity (optional)
In this section, we explore the impact of small deviations in "frequency modulation sensitivity" on the FMCW LiDAR system. By introducing these deviations, we can assess how they affect the accuracy and stability of the measured distance.
Run and results
Instructions for running the model and discussion of key results
Step 1: Setting up the FMCW Laser
- Open Step1_FMCW.icp .
- Open the script file Step1_FMCW_setup.lsf .
- Set appropriate time scales to check the visualizers.
In this step, we would export FMCW laser settings as well as the "time window" in environment setting for following steps.
The frequency modulation of the FMCW laser is defined via two inputs: “frequency modulation sensitivity” (unit Hz/V) and an external electrical time signal (unit V). The multiplication product of these two inputs determines the frequency modulation applied to the laser source. In this example, we define a triangular electrical time signal with a maximum value of 1V through a scripted source. This signal can be examined in Visualizer 2 (result of electrical oscilloscope OSC_1).
Next, we examine the output of the FMCW laser. By adjusting the time scale on the Visualizer 1 (result of optical oscilloscope OOSC_1), we can closely observe the FMCW time signal. The signal follows our defined pattern, starting from the base frequency (change of frequency = 0Hz), then increasing the frequency to its maximum, and dropping to the base frequency again at the end. This behavior confirms that the FMCW modulation is functioning as intended.
Step 2: System simulation
- Open Step2_lidar_circuit.icp
- Open Step2_lidar_circuit.lsf and check the speed, distance at line 15 &16.
Users need to first define the distance as well as the speed between the moving object and the source.(line 15& 16) The script would load files from step1 (FMCW setting), capture the phase change due to Doppler effect and run the simulation. After analyzing the result of RFSA_1, the distance and speed could be calculated using script commands and shown in the script prompt. The calculated distance and speed do agree with our settings at the beginning of this steps. Details about the theory could be found in appendix.
Step 3: Deviation due to nonlinear frequency modulation sensitivity (optional)
- Open nonlinearFMsensitivity_distance.icp .
- Run the script file nonlinearFMsensitivity_distance.lsf .
The script first defines frequency modulation sensitivity with a small sinusoidal deviation, then compare with the one without deviation to check system robustness.
As can be seen from the figure on the left, a nonlinear frequency modulation sensitivity will cause an uncertainty in measuring the distance of an object. The results are compared with a linear (constant) FM sensitivity case. The figure on the right shows the absolute error as a function of distance. This analysis helps users evaluate the reliability of the FMCW LiDAR system under varying conditions.
Important model settings
Description of important objects and settings used in this model
Sampling rate and df
In step 1, several settings are needed to configure a FMCW laser correctly. We set the simulation input as “sample rate” in “root element”. The time and frequency resolution are therefore:
$$ \Delta t=\frac{\text{time window}}{\text{number of samples}}=\frac{1}{\text{sample rate}} $$
$$ \Delta f=\frac{\text{sample rate}}{\text{number of samples}}=\frac{1}{\text{time window}} $$
In summary, ∆f should be much smaller than 2 f d so that two frequency peaks could be recognized by monitor RFSA. Therefore, "time window" should be set appropriately. Details about df and dt can be found in this page .
Phase change due to Doppler shift
When detecting a moving object, the frequency of the received signal changes from the original frequency because of the Doppler effect. This frequency shift results in an additional phase change. To capture this phase change, let us revisit the equation that describes the frequency difference due to Doppler effect:
$$ f_d=f_r-f=\frac{2v}{c}f $$
where f r is the frequency of the receiving signal while f is the original frequency, i.e. frequency of light. v is the velocity of the moving object in radial direction.
The additional phase change would be:
$$ \phi_d=\int f_d dt=\frac{2v}{c}f t$$
Apparently, the shift is a linear function with time. Therefore, we could not directly set one single “time delay” value in system simulation. One workaround here is to create an artificial voltage-phase relationship. Then, together with the ramp voltage time signal, the phase change could be mapped to time, which is illustrated in the following figure.
Updating the model
Instructions for updating the model based on your device parameters
Arbitrary frequency modulation
In this example, we applied a triangle frequency chirp function. However, FMCW laser object supports arbitrary electrical input signal. User could define their own function in the scripted electrical source.
Taking the model further
Information and tips for users that want to further customize the model
Multiple LiDARs
In this example, we only demonstrate one LiDAR, which could only recognize radial distance and velocity. To detect arbitrary moving direction, multiple FMCW lidars are needed.
Additional resources
Additional documentation, examples, and training material
See also
Related Ansys Innovation Courses
Appendix
Additional background information and theory
FMCW and spectrum of RFSA
In this section, we explain why the RFSA spectrum indicates the beat frequency of emitting and receiving signals and how to derive distance and speed from beat frequencies. Considering FMCW with linearly increasing frequency, the summation of the emitting and receiving becomes a beat signal.
First, the transmitted signal is:
$$ E_t(t)=Ae^{j\phi (t)}=Ae^{j\pi s t^2} $$
where A is the signal amplitude and s is the chirp rate.
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NOTE: The linearly increasing frequency leads to a quadratically varying phase. $$ f(t)=st $$ $$ \phi (t)=2\pi \int f(t)dt=\pi st^2 $$ |
The received signal is given by:
$$ E_r(t)=A_r e^{j\pi s (t-\tau)^2+j2\pi f_d t} $$
where A r is the received amplitude, τ is the time delay due to light traveling and f d is the Doppler frequency shift.
The output of the photodetector after adding both signals is:
$$ PD(t)=|E_t(t)+E_r(t)|^2=|Ae^{j\pi s t^2}+A_r e^{j\pi s (t-\tau)^2+j2\pi f_d t} |^2=A^2+{A_r}^2+2A A_r cos(2\pi (s\tau - f_d)t-\pi s {\tau}^2 ) $$
where the beat frequency is given by (sτ - f d ), which is then captured by the power spectrum monitor, RFSA. With the similar derivation, the beat frequency of decreasing frequency FMCW is (sτ + f d ).
$$ f_{b1}=s\tau - f_d $$
$$ f_{b2}=s\tau + f_d $$
In RFSA, we could find these two beat frequencies, f b1 & f b2 .
Since s , chirp rate, is defined by the user in the FMCW source, we could then obtain f d and τ:
$$ \tau=\frac{f_{b2}+f_{b1}}{2s} $$
$$ f_d=\frac{f_{b2}-f_{b1}}{2} $$
Then, the distance and the speed are:
$$ distance=\frac{\tau c}{2} $$
$$ v=\frac{f_d c}{2f} $$
where f is the frequency of light.