Signal Processing - March 2017 - 25
The FMCW radar transmits periodic wideband FM pulses,
whose angular frequency increases linearly during the pulse.
For the carrier frequency fc and FM modulation constant K , a
single FMCW pulse can be written as [see Figure 3(a)]
A typical decision strategy can be formulated based on statistical hypothesis testing (a target present or not). This leads to
a simple threshold testing at the matched filter output.
Range resolution, another key performance measure,
denotes the ability to distinguish closely spaced targets. Two
targets can be separated in the range domain only if they produce nonoverlapping returns in the time domain. Hence, the
range resolution is proportional to the pulsewidth T p . In other
words, finer pulses provide higher resolution. However, shorter
pulses contain less energy, which implies poor receiver signalto-noise ratio (SNR) and detection performance. As explained
in the section "Radar Waveforms," this problem is overcome
by the technique called pulse compression, which uses phase
or frequency modulated pulses.
s (t) = e j2r ( fc +0.5Kt) t
The signal reflected from a target is conjugately mixed with
the transmitted signal to produce a low-frequency beat signal,
whose frequency gives the range of the target. This operation
is repeated for P consecutive pulses. Two-dimensional (2-D)
waveforms in Figure 3(c) depict successive reflected pulses
arranged across two time indices. The slow time index p simply corresponds to pulse number. On the other hand, the fast
time index n assumes that for each pulse, the corresponding
continuous beat signal is sampled with frequency fs to collect
N samples within the time duration T. Assuming single target and neglecting reflected signal distortions, the FMCW
radar receiver output as a function of these two time indices is
given by
Velocity estimation
Estimation of the target velocity is based on the phenomenon
called the Doppler effect. Suppose the car displayed in Figure 2
is moving ahead with differential velocity v. With the existence
of relative motion between two cars, the reflected waves are
delayed by time x = (2 (R ! vt) /c) . The time dependent delay
term causes a frequency shift in the received wave known as the
Doppler shift fd = (! 2v/m) . The Doppler shift is inversely proportional to wavelength m , and its sign is positive or negative,
depending on whether the target is approaching or moving away
from the radar. While this frequency shift can be detected using
CW radar, it lacks the ability to measure the targets range. Here,
we discuss a pulsed radar configuration that uses frequency
modulated (FM) CW pulses and provides simultaneous rangevelocity estimation in multitarget traffic scenarios.
Frequency
f2
First Chirp
T
T0
Second
Chirp
TR
2fc R
E1 +~ (n, p) .
d (n, p) . exp ' j2r ;` 2K R + fd j n + fd pT0 +
c
fs
c
(5)
Therefore, as illustrated in Figure 3(c), discrete Fourier transform across fast time n can be applied to obtain beat frequency
fb = (2KR/c) coupled with Doppler frequency fd . This operation is also known as the range transform or range gating,
which allows the estimation of Doppler shift corresponding to
R = 20 m, Differential Vel = 20 mi/h
K = (f2-f1)/T
fb
τ
f1
R = 10 m, Differential Vel = 0
P th Chirp
Time
(a)
(b)
Doppler FFT Across P Range Transformed
Samples Yields Speed of Target at R1
P
2
1
Differential Speed (mi/h)
Slow
Time
30
Received
Signal
Range2
Doppler Plot
by 2-D FFT of 1
the Radar
Mixer Output
20
10
0
-10
0
10
20
Range (Meters)
30
(4)
0 # t # T.
P
Slow
Fast Time
Time
0 R1
0
N -1
Range
RN -1
Range FFT Across N Fast Time
Samples of the Radar Mixer Output
(c)
Figure 3. (a) A spectrogram of an FMCW waveform with modulation constant K = (B/T) , reset time TR, and pulse period T0; transmitting P successive chirps. Roundtrip delay x is converted to beat frequency fb. (b) Typical traffic scenario: stationary traffic sign, the radar, and passenger car moves at 20 mi/h (range and differential
velocity are displayed). (c) A 2-D joint range-Doppler estimation with 77-GHz FMCW radar {[N, P ] = [64, 64], SNR = 10 dB, BW = 300 MHz, T = 300 ns }.
IEEE SIgnal ProcESSIng MagazInE
|
March 2017
|
25
Table of Contents for the Digital Edition of Signal Processing - March 2017
Signal Processing - March 2017 - Cover1
Signal Processing - March 2017 - Cover2
Signal Processing - March 2017 - 1
Signal Processing - March 2017 - 2
Signal Processing - March 2017 - 3
Signal Processing - March 2017 - 4
Signal Processing - March 2017 - 5
Signal Processing - March 2017 - 6
Signal Processing - March 2017 - 7
Signal Processing - March 2017 - 8
Signal Processing - March 2017 - 9
Signal Processing - March 2017 - 10
Signal Processing - March 2017 - 11
Signal Processing - March 2017 - 12
Signal Processing - March 2017 - 13
Signal Processing - March 2017 - 14
Signal Processing - March 2017 - 15
Signal Processing - March 2017 - 16
Signal Processing - March 2017 - 17
Signal Processing - March 2017 - 18
Signal Processing - March 2017 - 19
Signal Processing - March 2017 - 20
Signal Processing - March 2017 - 21
Signal Processing - March 2017 - 22
Signal Processing - March 2017 - 23
Signal Processing - March 2017 - 24
Signal Processing - March 2017 - 25
Signal Processing - March 2017 - 26
Signal Processing - March 2017 - 27
Signal Processing - March 2017 - 28
Signal Processing - March 2017 - 29
Signal Processing - March 2017 - 30
Signal Processing - March 2017 - 31
Signal Processing - March 2017 - 32
Signal Processing - March 2017 - 33
Signal Processing - March 2017 - 34
Signal Processing - March 2017 - 35
Signal Processing - March 2017 - 36
Signal Processing - March 2017 - 37
Signal Processing - March 2017 - 38
Signal Processing - March 2017 - 39
Signal Processing - March 2017 - 40
Signal Processing - March 2017 - 41
Signal Processing - March 2017 - 42
Signal Processing - March 2017 - 43
Signal Processing - March 2017 - 44
Signal Processing - March 2017 - 45
Signal Processing - March 2017 - 46
Signal Processing - March 2017 - 47
Signal Processing - March 2017 - 48
Signal Processing - March 2017 - 49
Signal Processing - March 2017 - 50
Signal Processing - March 2017 - 51
Signal Processing - March 2017 - 52
Signal Processing - March 2017 - 53
Signal Processing - March 2017 - 54
Signal Processing - March 2017 - 55
Signal Processing - March 2017 - 56
Signal Processing - March 2017 - 57
Signal Processing - March 2017 - 58
Signal Processing - March 2017 - 59
Signal Processing - March 2017 - 60
Signal Processing - March 2017 - 61
Signal Processing - March 2017 - 62
Signal Processing - March 2017 - 63
Signal Processing - March 2017 - 64
Signal Processing - March 2017 - 65
Signal Processing - March 2017 - 66
Signal Processing - March 2017 - 67
Signal Processing - March 2017 - 68
Signal Processing - March 2017 - 69
Signal Processing - March 2017 - 70
Signal Processing - March 2017 - 71
Signal Processing - March 2017 - 72
Signal Processing - March 2017 - 73
Signal Processing - March 2017 - 74
Signal Processing - March 2017 - 75
Signal Processing - March 2017 - 76
Signal Processing - March 2017 - 77
Signal Processing - March 2017 - 78
Signal Processing - March 2017 - 79
Signal Processing - March 2017 - 80
Signal Processing - March 2017 - 81
Signal Processing - March 2017 - 82
Signal Processing - March 2017 - 83
Signal Processing - March 2017 - 84
Signal Processing - March 2017 - 85
Signal Processing - March 2017 - 86
Signal Processing - March 2017 - 87
Signal Processing - March 2017 - 88
Signal Processing - March 2017 - 89
Signal Processing - March 2017 - 90
Signal Processing - March 2017 - 91
Signal Processing - March 2017 - 92
Signal Processing - March 2017 - 93
Signal Processing - March 2017 - 94
Signal Processing - March 2017 - 95
Signal Processing - March 2017 - 96
Signal Processing - March 2017 - 97
Signal Processing - March 2017 - 98
Signal Processing - March 2017 - 99
Signal Processing - March 2017 - 100
Signal Processing - March 2017 - 101
Signal Processing - March 2017 - 102
Signal Processing - March 2017 - 103
Signal Processing - March 2017 - 104
Signal Processing - March 2017 - 105
Signal Processing - March 2017 - 106
Signal Processing - March 2017 - 107
Signal Processing - March 2017 - 108
Signal Processing - March 2017 - 109
Signal Processing - March 2017 - 110
Signal Processing - March 2017 - 111
Signal Processing - March 2017 - 112
Signal Processing - March 2017 - 113
Signal Processing - March 2017 - 114
Signal Processing - March 2017 - 115
Signal Processing - March 2017 - 116
Signal Processing - March 2017 - 117
Signal Processing - March 2017 - 118
Signal Processing - March 2017 - 119
Signal Processing - March 2017 - 120
Signal Processing - March 2017 - 121
Signal Processing - March 2017 - 122
Signal Processing - March 2017 - 123
Signal Processing - March 2017 - 124
Signal Processing - March 2017 - Cover3
Signal Processing - March 2017 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com