Signal Processing - March 2017 - 28

section for details). Due to the pulse
To elucidate advanced estimation techThe traffic imaging
compression, the range resolution is
niques, the dimensionality of the problem
problem can be turned
inversely proportional to the bandis reduced to two dimensions. It should be
into a classical parameter
width of the FMCW signal and is
noted that the discussed techniques can be
estimation problem so
independent of pulsewidth. For examextended to four-dimensional problems
that superresolution
ple, the short-range FMCW radar uses
with mobile targets and elevation direction.
techniques such as
ultrawideband (UWB) waveforms to
As discussed previously, the 2-D FFT of
measure small distances with higher
(8)
can provide joint estimation of distance
MuSiC can be applied.
resolution. The Doppler resolution is a
and angle. The FFT-based estimation has the
function of pulsewidth and the number of pulses used
least complexity of implementation, which is O (LN log LN) ,
for the estimation. Thus, with the ability to measure
where N is the number of time domain samples and L
both range and speed with high resolution, FMCW radar
denotes the number of elements in a one-dimensional (1-D)
is widely used in the automotive industry.
antenna array. However, the resolution of Fourier techniques
is dictated by the Rayleigh limit. While the higher range res■ In contrast to FMCW waveforms, the frequency of FSK
olution can be obtained with larger FMCW bandwidth, the
and SFCW varies in a discrete manner [see Figure 5(c)]. In
higher angular resolution requires more antenna elements,
this case, the range profile of the target and the data coladding to the cost of RF front end. Additionally, the radar
lected at discrete frequencies form the inverse Fourier
has to process a larger set of signal samples. However, it is
transform relationship. Also, hybrid waveform types can be
important to reduce the computational load while realizing
employed to achieve additive performance. FSK waveform
the desired angular and range resolution. We first visit the
can be combined with multislope FMCW waveform to
ML formulation of joint estimation of range and direction of
overcome ghost targets in radar processing [16]. Similarly,
targets. Then, we review the so-called superresolution techalternate pulses of CW and FMCW are used to accurately
niques as suboptimal and lower complexity alternatives to
estimate range and Doppler [17].
the ML estimator.
■ OFDM can be viewed as another multifrequency waveform that offers unique features of the joint implementation of automotive radar and vehicle-to-vehicle
ML estimation
communications [18], [19]. For the radar operation, the
The complex Gaussian observation noise in (8) is assumed
orthogonality between OFDM subcarriers is ensured by
to be temporally and spatially independent. ML estimation
choosing carrier spacing more than maximum Doppler
of 2-D parameters (R, i) can be found solving the followshift, and the cyclic prefix duration is selected greater than
ing equation:
the longest round-trip delay [see Figure 5(d)]. The range
Q -1
L -1 N -1
2K R q n
profile is estimated through frequency domain channel
min / / d (l, n) - / a q exp ' j2r ;
R q, i q
c
fs
estimation. OFDM radar processing along with simulation
q =0
l =0 n =0
results is explained in [20].
fc ld sin i q 2fc R q 2
E1 .
+
+
Based on the knowledge of target statistics, radar wavec
c
forms can be optimized. Radar waveform design is revisited
(9)
along with multiple-input, multiple-output (MIMO) radars in
the "MIMO Radar" section.
Thus, depending on the granularity of (R, i) search space, the
ML estimator can offer the resolution beyond the Rayleigh limit
set by system parameters such as bandwidth and number of
Advanced estimation techniques
antenna elements. However, the complexity of implementing
Advancements in silicon semiconductor technology have had
this algorithm depends on the cardinality of the search-space as
the profound impact on the design of automotive radar syswell as the number of targets. Since (R q, i q) are continuous
tems, providing higher integration and performance at lower
cost. This section reviews some sophisticated radar signal proparameters, the computational complexity of ML algorithm
cessing algorithms, which have become feasible with such
O (| (R, i) | Q) becomes prohibitive. In the subsequent paraadvancements, especially for real-time implementation. In this
graphs, the superresolution techniques that can achieve high ressection, most commonly used FMCW radar architecture is
olution at lower computational cost are illustrated.
assumed and targets are considered to be stationary. Hence, (7)
is reduced to a range-azimuth estimation problem with the sigSuperresolution techniques
nal model given by
Due to their prohibitive computational cost, ML algorithms
need to be implemented via suboptimal techniques. These techniques rely on collecting enough signal samples. At a suffiQ -1
fc ld sin i q
2K R q n
ciently high SNR, eigenvalues and associated eigenvectors of
d (l, n) . / a q exp ' j2r ;
+
c fs
c
q =0
sample covariance matrix C (defined in Algorithm 1) repre2fc R q
sent
the ML estimate of their true values. Hence, these eigenE1 + ~ (l, n) .
+
(8)
c
vectors can be used to resolve the target with high resolution.
28

IEEE SIgnal ProcESSIng MagazInE

March 2017

Table of Contents for the Digital Edition of Signal Processing - March 2017