import radarsimpy
radarsimpy.__version__

'8.2.0'

PMCW Radar

This is a phase-modulated continuous-wave (PMCW) radar simulation example based on RadarSimPy.

Radar Model

Phase code

The phase codes in the transmitter channels are defined with phs and t_mod. amp can also be used if there is an amplitude modulation.

In this example, 2 binary phase code sequences are assigned to 2 different transmitter channels.

import numpy as np

code1 = np.array([1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1,
                  1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1,
                  1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1,
                  -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1,
                  1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1,
                  1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1,
                  1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1,
                  -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1,
                  -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1,
                  1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1,
                  1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1,
                  -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1,
                  -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1,
                  -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1,
                  1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1,
                  1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1])
code2 = np.array([1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1,
                  -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1,
                  -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1,
                  -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1,
                  1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1,
                  -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1,
                  1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1,
                  1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1,
                  -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1,
                  -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1,
                  1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1,
                  1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1,
                  -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1,
                  -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1,
                  1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1,
                  -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1])

phase_code1 = np.zeros(np.shape(code1))
phase_code2 = np.zeros(np.shape(code2))
phase_code1[np.where(code1 == 1)] = 0
phase_code1[np.where(code1 == -1)] = 180
phase_code2[np.where(code2 == 1)] = 0
phase_code2[np.where(code2 == -1)] = 180

t_mod1 = np.arange(0, len(phase_code1))*4e-9
t_mod2 = np.arange(0, len(phase_code2))*4e-9

Plot the phase code sequences

import plotly.graph_objs as go
from IPython.display import SVG, display

fig = go.Figure()

fig.add_trace(go.Scatter(
    x=t_mod1,
    y=phase_code1,
    name='Phase code 1',
))
fig.add_trace(go.Scatter(
    x=t_mod2,
    y=phase_code2,
    name='Phase code 2',
))

fig.update_layout(
    title='Phase modulation sequences',
    yaxis=dict(title='Phase (deg)'),
    xaxis=dict(title='Time (s)'),
)

# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))

Transmitter

Setup the basic transmitter parameters through Transmitter module.

The following table lists the parameters in this example.

Parameter	Variable in Transmitter	Value
Frequency ($f$)	f	24.125 GHz
Time ($T$)	t	2.1e-6 s
Transmitted power ($P_t$)	tx_power	20 dBm
Number of pulses	pulses	256

There are 2 transmitter channels assigned with 2 different phase code sequences. The location of these 2 transmitter channels have 1 m offset in x-axis.

from radarsimpy import Radar, Transmitter, Receiver

tx_channel_1 = dict(
    location=(0, 0, 0),
    mod_t=t_mod1,
    phs=phase_code1,
)

tx_channel_2 = dict(
    location=(1, 0, 0),
    mod_t=t_mod2,
    phs=phase_code2,
)

tx = Transmitter(f=24.125e9,
                 t=2.1e-6,
                 tx_power=20,
                 pulses=256,
                 channels=[tx_channel_1, tx_channel_2])

Receiver

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	250 Msps
Noise figure ($NF$)	noise_figure	10 dB
RF gain/loss ($G_{rf}$)	rf_gain	20 dB
Load resistor ($R_L$)	load_resistor	1000 $\Omega$
Baseband voltage gain ($G_{BB}$)	baseband_gain	30 dB

rx = Receiver(fs=250e6,
              noise_figure=10,
              rf_gain=20,
              baseband_gain=30,
              load_resistor=1000,
              channels=[
                  dict(location=(0, 0, 0))
              ])

Create the FMCW radar model based on all the parameters defined above.

radar = Radar(transmitter=tx, receiver=rx)

Targets

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=(20, 0, 0),
                speed=(-200, 0, 0),
                rcs=20,
                phase=0)

target_2 = dict(location=(70, 0, 0),
                speed=(0, 0, 0),
                rcs=35,
                phase=0)

target_3 = dict(location=(33, 10, 0),
                speed=(100, 0, 0),
                rcs=20,
                phase=0)

targets = [target_1, target_2, target_3]

Simulate Baseband Signals

Use the simulator module to simulate the baseband samples. The user can choose between Python engine simpy or C++ engine simc.

The output baseband data is a 3-D matrix:

$[channels, pulses, ADC~samples]$

# Python engine
from radarsimpy.simulator import simpy
# C++ engine
from radarsimpy.simulator import simc

data = simc(radar, targets, noise=True)
time_matrix = data['timestamp']
data_matrix = data['baseband']

For convenience, the baseband signal for these 2 transmitter channels are separated. So the total size of the baseband data matrix is $2 \times pulses \times samples$.

The baseband of the 2 transmitter channels are simulated separated. For a realistic case, these 2 transmitter channels should tranmit simutaneously. Thus, the baseband of these 2 channels need to be added together

baseband = data_matrix[0, :, :]+data_matrix[1, :, :]

Plot the baseband samples

fig = go.Figure()

fig.add_trace(go.Scatter(
    x=time_matrix[0, 0, :],
    y=np.real(baseband[0, :]),
    name='I',
))
fig.add_trace(go.Scatter(
    x=time_matrix[0, 0, :],
    y=np.imag(baseband[0, :]),
    name='Q',
))

fig.update_layout(
    title='I/Q Baseband Signals',
    yaxis=dict(title='Amplitude (V)'),
    xaxis=dict(title='Time (s)'),
)

# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))

Radar Signal Processing

Demodulate the 2 channels separately

Channel 1

range_profile = np.zeros(
    (radar.channel_size, radar.transmitter.pulses, 255), dtype=complex)

for pulse_idx in range(0, radar.transmitter.pulses):
    for bin_idx in range(0, 255):
        range_profile[0, pulse_idx, bin_idx] = np.sum(
            code1*baseband[pulse_idx, bin_idx:(bin_idx+255)])

Channel 2

for pulse_idx in range(0, radar.transmitter.pulses):
    for bin_idx in range(0, 255):
        range_profile[1, pulse_idx, bin_idx] = np.sum(
            code2*baseband[pulse_idx, bin_idx:(bin_idx+255)])

Plot range profiles

bin_size = 3e8/2*4e-9
range_bin = np.arange(0, 255, 1)*bin_size

fig = go.Figure()

fig.add_trace(go.Scatter(
    x=range_bin,
    y=20 * np.log10(np.mean(np.abs(range_profile[0, :, :]), axis=0)),
    name='Channel 1, averaged pulses',
))
fig.add_trace(go.Scatter(
    x=range_bin,
    y=20 * np.log10(np.mean(np.abs(range_profile[1, :, :]), axis=0)),
    name='Channel 2, averaged pulses',
))

fig.update_layout(
    title='Range profile',
    yaxis=dict(title='Amplitude (dB)'),
    xaxis=dict(title='Range (m)'),
)

# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))

Doppler processing

from scipy import signal

doppler_window = signal.chebwin(radar.transmitter.pulses, at=50)

range_doppler = np.zeros(np.shape(range_profile), dtype=complex)
for ii in range(0, radar.channel_size):
    for jj in range(0, 255):
        range_doppler[ii, :, jj] = np.fft.fftshift(np.fft.fft(
            range_profile[ii, :, jj] * doppler_window,
            n=radar.transmitter.pulses,
        ))
unambiguous_speed = 3e8 / radar.transmitter.prp / \
    radar.transmitter.fc_vect[0] / 2

Plot range-Doppler map

range_axis = np.arange(0, 255, 1)*bin_size

doppler_axis = np.linspace(
    -unambiguous_speed/2, unambiguous_speed/2, radar.transmitter.pulses, endpoint=False)

fig = go.Figure()
fig.add_trace(go.Surface(x=range_axis, y=doppler_axis, z=20 *
              np.log10(np.abs(range_doppler[0, :, :])), colorscale='Rainbow'))


fig.update_layout(
    title='Range Doppler',
    height=800,
    scene=dict(
        xaxis=dict(title='Range (m)'),
        yaxis=dict(title='Velocity (m/s)'),
        zaxis=dict(title='Amplitude (dB)'),
        aspectmode='cube',
    ),
)

# fig.show()
display(SVG(fig.to_image(format='svg', scale=1)))