Signal Processing - March 2017 - 39

Automotive use case

High-resolution processing
High-resolution frequency estimation is theoretically able to
resolve multiple targets if the frequencies are distinct in at least
one dimension. Other works in automotive radar typically focus
on high-resolution frequency estimation in the angular dimension. We point out that in critical use cases, as described in the
section "Automotive Use Case," it can be advantageous to also
consider the range and relative velocity dimension for high-resolution processing. In the following, we develop a framework to
exploit the frequency separation in all three dimensions.
An optimal approach for high-resolution frequency estimation is to estimate all three frequency dimensions jointly, which
is computationally demanding due to the large parameter
space. In automotive radar, computational efficiency is crucial
to ensure fast system reactions for ADASs and for future HAD

Mirror

Target

x-Position
(a)
2.0
Normalized Separation

In most automotive scenarios, the targets are well separated,
i.e., their associated frequency differences exceed the
periodogram's resolution limit in at least one dimension.
However, specular multipath propagation can give rise to target pairs with frequency separation below the resolution limits in all three dimensions. In those cases, conventional
processing fails, and high-resolution techniques become necessary. We give an example of such a multipath scenario,
which constitutes a typical ACC or FCA use case.
Figure 1(a) shows a subject vehicle overtaking a slower target vehicle on a two-lane highway in a country where driving
on the right is the norm. In this setup, the radar receives not
only a direct target return, but also an indirect target return
via the guard rail. The corresponding propagation paths are
shown as dashed lines in Figure 1(a). This phenomenon is
known as specular multipath propagation and leads to a mirror
target in the radar return.
For calculating the range, relative velocity, and angular
separation between the original target and the mirror target,
we consider a lane width of 3.75 m, a center guard rail, a subject vehicle speed of 100 km/h, and a target vehicle speed of
80 km/h. We map the parameter separation to normalized
frequency separation using the system parameters, gathered in
Table 1, of a typical series-production automotive radar sensor.
Figure 1(b) shows the frequency separations normalized to the
respective resolution limit over the relative x-position of the
target. The shape of the angular separation stems from undersampling in the angular dimension, as multiple angular hypotheses for the original and mirror target have to be considered.
Observe that above 130 m and between 25 m and 42 m,
the frequency separation is below the respective resolution
limit in all three dimensions, so that the periodogram will
fail to resolve the original and mirror target. This can lead to
misplaced target estimates in the driving path of the subject
vehicle and may trigger erroneous ACC or FCA reactions such
as deceleration or even emergency braking. This holds in particular for small x-positions in the region from 25 m to 42 m.
To cope with such scenarios, we next present a framework for
high-resolution frequency estimation.

Range λ
Relative Velocity µ
Angle ν

1.5
1.0
0.5
0.0
20

80
100
x-Position (m)
(b)

120

140

Figure 1. The two-target example: (a) the practically relevant scenario
for ACC or FCA and (b) a corresponding normalized frequency separation. For the mapping of range, relative velocity, and angle to normalized
frequencies, the radar system parameters in Table 1 are used.

applications. A common approach to reduce the computational
complexity is to decouple the multidimensional frequency estimation into a sequence of 1-D frequency estimation problems.
Note that a key result of [43] and [44] is that the decoupled
approach can achieve almost the same estimation performance
but with a significant reduction in computational cost. When
decoupling the 3-D frequency estimation, one has to decide
on the processing sequence. In one dimension, referred to as
resolution dimension, a 1-D high-resolution frequency estimation of K targets has to be performed first. In the remaining
dimensions, the calculated frequency estimates can then be
used for signal component extraction, so that the remaining
estimation problem is further simplified into K single-target
frequency estimation problems. Note that the computational
cost is dominated by the 1-D high-resolution frequency estimation of K targets in the resolution dimension. The subsequent single-target frequency estimators can be calculated by
an computationally efficient periodogram-like approach.
The overall success of a decoupled approach depends
critically on resolved estimates in the resolution dimension.
It is well known that the resolution success of 1-D high-resolution frequency estimation depends on the available signalto-noise ratio and particularly on the frequency separation.
This holds for parametric approaches methods [18] as well
as for compressed sensing approaches [20]. Therefore, the
correct selection of the resolution dimension is crucial for

IEEE SIgnal ProcESSIng MagazInE

March 2017

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