IEEE Solid-States Circuits Magazine - Spring 2022 - 46

10 MHz
Windowing
Range FFT
Doppler FFT
MIMO Processing
ADC Filter
Frac-N PLL
Up-Converter
Synchronization
f0 + B
Transmit
Chirp
υres
φres
Rres
f0
∆t
FFT Time
Sampling Moments
10-40 µs
Range Gates (1,024 Typical)
Range
FFT
FIGURE 2: The fast-chirp FMCW signal processing and transceiver architecture. Frac-N: fractional-N.
single chirp. Windowing improves
the peak-to-sidelobe ratio for
the
easier detection of weak targets at
the cost of a loss in the range resolution.
The output from all the chirps
in the frame is stored to perform a
second Doppler FFT on ND
samples,
corresponding to equal distance to
the extract velocities, which boosts
target over noise power with a total
TABLE 1. BASIC RADAR EQUATIONS.
PARAMETER
EQUATION
Range resolution
Maximum range
Velocity resolution
Maximum velocity
Beat frequency
Angular resolution
R =res
R
max
=
v =res
v
f
c
2
B
.
cf T
2
m
2Tmeas
max = m PRF
4
beat =
zres
=
T
B x
chirp
NN
50 7
.
TX rx
N chirp
B
.
(1)
(2)
(3)
(4)
(5)
(6)
processing gain of 10 log NN dB.RD10
Multiple antenna signal streams form
a third dimension for the detection
of the angle of arrival, as will be
detailed in later sections. The resulting
data cube is a quantized representation
of the observation scene of
the radar in space and velocity. Pixel
dimensions represent resolution
with a given sensitivity, which must
exceed a certain threshold value for
reliable detection. Radar signal processing
algorithms operate on the
dimensions of the cube.
Radar design is subject to multiple
COMMENTS
co: speed of light
B: modulation bandwidth
ff/:2Ns Nyquist frequency for max range
f :s
=
sampling rate
T :chirp
m: wavelength
T :meas
chirp duration,
measurement time
Pulse repetition frequency (PRF)
x: propagation delay
Assuming 90!
N :TX
N :XR
46
c FoV and a virtual array
transmit antennas
receive antennas
SPRING 2022
IEEE SOLID-STATE CIRCUITS MAGAZINE
tradeoffs within and across the waveform,
antenna, and circuit domains.
For example, assuming a long-range
radar scenario, chirps need to be far
apart to avoid range ambiguities for a
long range in (3), but for high maximum
unambiguous velocity, they
need to be close together. Long chirps
and long measurement times improve
sensitivity and velocity resolution,
respectively, but this makes chirps
from the same sequence measure
the same object at different ranges,
resulting in range migration and
the loss of sensitivity. For example,
detecting a motorcycle with a relative
speed of 200 km/h with a 20-ms chirp
sequence using a 500-MHz modulation
bandwidth (0.3-m resolution)
makes it move almost four range bins
within the same sequence, limiting
the sensitivity benefits of long chirps.
The keystone transformation could
mitigate range migration at the cost
Time
∆f
Received Echo
Chirp
Frame
∆f
76-81 GHz
I
Q
Phase Control
Azimuth Resolution,
e.g., 1°
υ
Field of View,
e.g., 45°
υ
Range
Resolution
Detection Range
e.g., 200 m
Number of Chirps (256 Typical)
Range Gate Slice
Doppler
FFT
Doppler
FFT
Doppler
FFT
Sensitivity
Frequency
Angular Processing
Number of Antennas

IEEE Solid-States Circuits Magazine - Spring 2022

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Spring 2022