import radarsimpy
radarsimpy.__version__
'10.0.0'
RadarSimPy supports the simulation of any arbitrary waveforms. You can specify the waveform by defining the frequency versus time curve. One of the example of using the arbitrary waveform feature is simulating the effect of a non-linear chirp in an FMCW radar.
The chirp can be defined by frequency versus time.
import numpy as np
freq_nonlinear = np.array([
2.40750000e+10, 2.40760901e+10, 2.40771786e+10, 2.40782654e+10,
2.40793506e+10, 2.40804341e+10, 2.40815161e+10, 2.40825964e+10,
2.40836750e+10, 2.40847521e+10, 2.40858275e+10, 2.40869012e+10,
2.40879734e+10, 2.40890439e+10, 2.40901127e+10, 2.40911800e+10,
2.40922456e+10, 2.40933096e+10, 2.40943719e+10, 2.40954326e+10,
2.40964917e+10, 2.40975491e+10, 2.40986049e+10, 2.40996591e+10,
2.41007117e+10, 2.41017626e+10, 2.41028119e+10, 2.41038595e+10,
2.41049055e+10, 2.41059499e+10, 2.41069927e+10, 2.41080338e+10,
2.41090733e+10, 2.41101111e+10, 2.41111473e+10, 2.41121819e+10,
2.41132149e+10, 2.41142462e+10, 2.41152759e+10, 2.41163039e+10,
2.41173304e+10, 2.41183552e+10, 2.41193783e+10, 2.41203999e+10,
2.41214198e+10, 2.41224380e+10, 2.41234546e+10, 2.41244696e+10,
2.41254830e+10, 2.41264947e+10, 2.41275048e+10, 2.41285133e+10,
2.41295202e+10, 2.41305254e+10, 2.41315289e+10, 2.41325309e+10,
2.41335312e+10, 2.41345298e+10, 2.41355269e+10, 2.41365223e+10,
2.41375161e+10, 2.41385082e+10, 2.41394987e+10, 2.41404876e+10,
2.41414748e+10, 2.41424605e+10, 2.41434444e+10, 2.41444268e+10,
2.41454075e+10, 2.41463866e+10, 2.41473640e+10, 2.41483399e+10,
2.41493140e+10, 2.41502866e+10, 2.41512575e+10, 2.41522268e+10,
2.41531945e+10, 2.41541605e+10, 2.41551249e+10, 2.41560876e+10,
2.41570488e+10, 2.41580083e+10, 2.41589661e+10, 2.41599224e+10,
2.41608770e+10, 2.41618299e+10, 2.41627812e+10, 2.41637309e+10,
2.41646790e+10, 2.41656254e+10, 2.41665702e+10, 2.41675134e+10,
2.41684550e+10, 2.41693949e+10, 2.41703331e+10, 2.41712698e+10,
2.41722048e+10, 2.41731381e+10, 2.41740699e+10, 2.41750000e+10])
t_nonlinear = np.linspace(0, 80e-6, 100)
Plot the non-linear chirp
import plotly.graph_objs as go
from IPython.display import SVG, display
fig = go.Figure()
fig.add_trace(go.Scatter(
x=np.linspace(0, 80e-6, 100)*1e6,
y=freq_nonlinear/1e9,
name='Non-linear chirp',
))
fig.add_trace(go.Scatter(
x=np.array([0, 80e-6])*1e6,
y=np.array([24.125e9-50e6, 24.125e9+50e6])/1e9,
name='Linear chirp',
))
fig.update_layout(
template="seaborn",
yaxis=dict(tickformat='.2f', title='Frequency (GHz)'),
xaxis=dict(tickformat='.2f', title='Time (us)'),
)
# fig.show()
# fig.write_image('arb_wavefrom.svg', height=400, width=600)
display(SVG(fig.to_image(format='svg', scale=1)))
Setup the basic transmitter parameters through Transmitter module.
For comparison, we created a linear chirp transmitter and a non-linear chirp transmitter.
from radarsimpy import Radar, Transmitter, Receiver
tx_channel = dict(
location=(0, 0, 0),
)
tx_nonlinear = Transmitter(f=freq_nonlinear,
t=np.linspace(0, 80e-6, 100),
tx_power=60,
prp=100e-6,
pulses=1,
channels=[tx_channel])
tx_linear = Transmitter(f=[24.125e9-50e6, 24.125e9+50e6],
t=[0, 80e-6],
tx_power=60,
prp=100e-6,
pulses=1,
channels=[tx_channel])
Setup the receiver parameters through Receiver module.
The parameters of the receiver are listed in the table below.
| Parameter | Variable in Receiver |
Value |
|---|---|---|
| Sampling rate ($f_s$) | fs |
2 Msps |
| Noise figure ($NF$) | noise_figure |
12 dB |
| RF gain/loss ($G_{rf}$) | rf_gain |
20 dB |
| Load resistor ($R_L$) | load_resistor |
500 $\Omega$ |
| Baseband voltage gain ($G_{BB}$) | baseband_gain |
30 dB |
rx_channel = dict(
location=(0, 0, 0),
)
rx = Receiver(fs=2e6,
noise_figure=12,
rf_gain=20,
load_resistor=500,
baseband_gain=30,
channels=[rx_channel])
Create the FMCW radar model based on all the parameters defined above.
radar_nonlinear = Radar(transmitter=tx_nonlinear, receiver=rx)
radar_linear = Radar(transmitter=tx_linear, receiver=rx)
The propertities of targets are defined here. There are 3 targets in this simulation. The locations of the targets are defined through $(x, y, z)$ coordinates in meters, and the speeds of the targets are defined trough $(v_x, v_y, v_z)$ in $m/s$. The propertites of the targets also includes radar cross-section (RCS (dBsm)) and phase (degree).
target_1 = dict(location=(200, 0, 0), speed=(-5, 0, 0), rcs=30, phase=0)
target_2 = dict(location=(95, 20, 0), speed=(-50, 0, 0), rcs=25, phase=0)
target_3 = dict(location=(30, -5, 0), speed=(-22, 0, 0), rcs=15, phase=0)
targets = [target_1, target_2, target_3]
from radarsimpy.simulator import simc
data_nonlinear = simc(radar_nonlinear, targets, noise=True)
time_matrix_nonlinear = data_nonlinear['timestamp']
data_matrix_nonlinear = data_nonlinear['baseband']
data_linear = simc(radar_linear, targets, noise=True)
time_matrix_linear = data_linear['timestamp']
data_matrix_linear = data_linear['baseband']
Plot baseband samples
fig = go.Figure()
fig.add_trace(go.Scatter(
x=time_matrix_nonlinear[0, 0, :] * 1e6,
y=np.real(data_matrix_nonlinear[0, 0, :]),
name='I nonlinear',
))
fig.add_trace(go.Scatter(
x=time_matrix_nonlinear[0, 0, :] * 1e6,
y=np.imag(data_matrix_nonlinear[0, 0, :]),
name='Q nonlinear',
))
fig.add_trace(go.Scatter(
x=time_matrix_linear[0, 0, :] * 1e6,
y=np.real(data_matrix_linear[0, 0, :]),
name='I linear',
))
fig.add_trace(go.Scatter(
x=time_matrix_linear[0, 0, :] * 1e6,
y=np.imag(data_matrix_linear[0, 0, :]),
name='Q linear',
))
fig.update_layout(
template="seaborn",
title='I/Q Beat Signals for the First Chirp',
yaxis=dict(title='Amplitude (V)'),
xaxis=dict(title='Time (µs)'),
)
# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))
from scipy import signal
import radarsimpy.processing as proc
range_window = signal.chebwin(radar_linear.samples_per_pulse, at=60)
range_profile_nonlinear = proc.range_fft(
data_matrix_nonlinear[:, :, :], range_window)
range_profile_linear = proc.range_fft(
data_matrix_linear[:, :, :], range_window)
Plot the range profile
max_range = (3e8 * radar_linear.receiver.fs *
radar_linear.transmitter.pulse_length /
radar_linear.transmitter.bandwidth / 2)
range_axis = np.linspace(
0, max_range, radar_linear.samples_per_pulse, endpoint=False)
fig = go.Figure()
fig.add_trace(go.Scatter(
x=range_axis,
y=20 * np.log10(np.abs(range_profile_nonlinear[0, 0, :])),
name='Nonlinear chirp',
))
fig.add_trace(go.Scatter(
x=range_axis,
y=20 * np.log10(np.abs(range_profile_linear[0, 0, :])),
name='Lineaer chirp',
))
fig.update_layout(
template="seaborn",
yaxis=dict(title='Amplitude (dB)'),
xaxis=dict(title='Range (m)'),
)
# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))