Signal Processing - March 2017 - 26

Y
R

d

Antenna Array
l

R
R

X

θ
Z

First Target
(R1, θ1, v1)
(a)

q thTarget
(Rq, θq, vq)
(b)

Figure 4. (a) A typical traffic scenario with reflections from different targets, including two cars at the same distance R. (b) The azimuth angle estimation
setup using uniform linear antenna array.

unique range gate by the application of second Fourier transform
across the slow time. A range-Doppler map can be found efficiently by using 2-D fast Fourier transform (FFT) (5). A demonstrative example based on the aforementioned discussion is
shown in Figure 3.

Direction estimation
Use of wideband pulses such as FMCW provides discrimination of targets in both distance and velocity. The discrimination in direction can be made by means of an antenna array.
Figure 4(a) depicts a realistic traffic scenario with several targets surrounding the radar that collects direct and multipath
reflections from them. In such cases, to spatially resolve equidistant targets and deliver comprehensive representation of
the traffic scene, angular location of targets should be estimated. Therefore, in automotive radars, the location of a target is often described in terms of a spherical coordinate
system (R, i, z), where (i, z) denote azimuthal and elevation
angles, respectively. However, in this case, the single antenna
radar setup as used in the range-velocity estimation problems
may not be sufficient, since the measured time delay
x = (2 (R ! vt) /c) lacks the information in terms of angular
locations of the targets.
To enable direction estimation, the radar should collect
reflected wave data across multiple distinct dimensions. For
example, locating a target using EM waves in 2-D requires the
reflected wave data from the object to be collected in two distinct dimensions. These distinct dimensions can be formed in
many ways using combinations of time, frequency, and space.
For instance, a linear antenna array and wideband waveforms
such as FMCW form two unique dimensions [13], [14]. Additionally, smaller wavelengths in mm-wave bands correspond to
smaller aperture sizes and, thus, many antenna elements can
be densely packed into an antenna array. Hence, the effective
radiation beam, which is stronger and sharper, in turn increases the resolution of angular measurements.
Consider an antenna array located in plane z = 0, and let l
be the abscissa corresponding to each receiver antenna position
26

[see Figure 4(b)]. Let (R q, i q) be the position of the qth target in spherical coordinates, moving with velocity v q relative
to the radar. With the help of far field approximation [15], for
the qth target, the round-trip time delay between a transmitter
located at the origin and the receiver positioned at coordinate
l is given by
x lq =

2 (R q + v q t) + ld sin i q
,
c

(6)

where d is the distance between antenna elements (usually
half the wavelength) arranged in a linear constellation. Combining (5) and (6) gives the three-dimensional (3-D) FMCW
radar output signal, which enables estimation of range, velocity, and angle. For Q number of targets, the signal can be represented as
Q -1

d (l, n, p) .

/

q =0

a q exp ' j2r ;c

fc ld sin i q
2K R q
+ fdq m n +
c
fs
c

+ fdq pT0 +

2fc R q
E1 + ~ (l, n, p),
c

(7)

where a and ~ correspond to same quantities as explained in
the range estimation problem. The delay term x lq creates uniform phase progression across antenna elements, which permits the estimation of the angle by FFT in spatial domain, as
shown in (7). Thus, 2-D location (range and angle) and speed
of targets can be jointly estimated by 3-D FFT. The target
location and velocity estimation problems are revisited later in
the section "Advanced Estimation Techniques" with more
emphasis on the high resolution algorithms and computational
complexity analysis.

Radar waveforms
Various automotive radar classes, summarized in Table 1,
have diverse specifications in terms of several fundamental
radar system performance metrics, such as range resolution,
velocity resolution, angular direction, SNR, and the probability of target detection. The type of waveform employed by a

IEEE SIgnal ProcESSIng MagazInE

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March 2017

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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
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Signal Processing - March 2017 - Cover3
Signal Processing - March 2017 - Cover4
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