An intimate look into how a DSP determines the course of action for a vehicle radar

Engineering Architect, Cadence Design Systems

in automotive electronics has driven the next leap of innovation in
transportation, fueled by a fundamental premise: In automotive applications, vehicles
must be able to sense their environment accurately.

cars must accurately sense not only their own distance, speed, and direction,
but also the distance, speed, and direction of any object that could cross
their path. Radar is the best way to gather that data, and these automotive
systems must successfully interpret the data to make life-and-death decisions.

How radar works

find out whether there is an object nearby that may affect the car, the
automotive system must determine direction or angle of arrival (AoA), speed and
distance of the object, and whether the object detected is real or a “false
positive” from noise or clutter in the background. Fig. 1
shows how the radar data is gathered.


Fig. 1: Block diagram of a radar system.

  1. A digital
    transmit signal is generated and converted into analog format and the
    transmitter signals (TX).
  2. These signals are
    released from the transmit antennas and into the environment.
  3. The signals
    “bounce” or reflect back to the receiver (RX) and are converted back into
    digital data by an analog-to-digital converter (ADC).
  4. The data is then
    processed by the digital signal processor (DSP) to make decisions based on that

DSP: determining whether to stop

values that influence the decision-making process performed by the DSP include
three main factors, as shown in Fig. 2:

  1. Direction: In the
    processing flow, the samples from the input data cube are filtered using a
    spatial beamforming filter to create digital beams as a part of the digital
    beamforming (DBF) module.
  2. Speed and
    distance: These beams are further processed by a 2D fast Fourier transform
    (FFT) algorithm along the range and Doppler axis.
  3. CFAR: Constant
    false alarm rate, or CFAR, works as a “filter” to determine whether a detected
    object is likely to be a real object or is part of the background “noise.”



Fig. 2: The DSP block diagram and flow.

an efficient implementation, the processor must perform data processing and
data transfers concurrently. The software should be structured to minimize the
data transfers, and the direct memory access (DMA) should be used to perform
the data transfers concurrently with module computations.


A. Beamforming for direction

DBF kernel performs finite impulse response (FIR) filtering along the channel
dimension in the data cube. The length of the FIR filter is equal to the number
of antenna elements — eight, in this case — and the FIR taps are pre-chosen to
pass signals from a beam centered on a particular pre-determined spatial
direction and to suppress signals from other directions.

practice, the DBF processes the data cube as input and produces a range-Doppler
2D signal as an output beam. Different sets of FIR taps can be used to generate
multiple beam signals using the same data cube. In this example, five beams are
generated along different directions using separate sets of FIR taps.

B. Doppler and range FFT for speed and

radar uses a 2D frequency-domain spectrum in the range-Doppler dimensions for
its processing. This spectrum is obtained by performing a 2D FFT — 1D FFT along
the range dimension, followed by 1D FFT along the Doppler dimension — and, thus,
forming the cube shown in Fig. 2.

2D range-Doppler FFT kernel is used to transform each of the five 2D beam
signals produced by the DBF kernel to a 2D frequency-domain spectrum. A
windowed 2D FFT is used to separate the signals, with the range FFTs along the
range dimension, followed by Doppler FFTs along the Doppler dimension. Each 1D FFT
also uses a Hamming window.

range FFT is computed as a 1D FFT, whereas the Doppler FFT is performed as a
block-based FFT to avoid transposing the input and output. The FFT algorithm is
based on the Kronecker product-based formalization. In the last stage, the
Doppler FFT kernel computes a point-wise energy of each bin.

C. CFAR for target detection

role of the CFAR is to determine the threshold, above which any return can be
considered to probably originate from a target. If this threshold is too low,
then more targets are detected at the expense of increased numbers of false

if the threshold is too high, then fewer targets are detected, but the number
of false alarms is also low. In most radar detectors, this threshold is
determined algorithmically to calculate the probability of a false alarm — or
equivalently, false alarm rate or time between false alarms.

CFAR kernel operates on a 2D energy signal in the frequency domain, classifying
each bin or cell under test (CUT) in the 2D FFT energy signal either as a
target (positive) or noise/clutter by comparing each CUT with a scaled estimate
of noise and clutter. The scale factor and threshold used are determined by the
probability of false alarm, or CFAR.


Fig. 3: The CFAR diagram showing
positive result and detection exceeding the threshold.

Fig. 3, the well-modulated CFAR is the threshold,
and the “positive” is where the detection exceeds the threshold. In other
words, to determine a target, the value of the CUT is compared with the CFAR —
the threshold calculated to determine the levels of the noise floor around the

is computed by examining a block of cells around the CUT (Fig. 4).
To avoid corrupting this estimate with values from the CUT itself, cells
adjacent to the CUT, or guard cells, are normally ignored. A target is declared
present in the CUT if its value is greater than all of its adjacent cells —
CFAR or noise-and-clutter threshold.


Fig. 4: The CFAR block processing.

CFAR kernels are distinguished by how the noise estimate is formed using the
training cells. For example, the cell-averaging constant false alarm rate
(CA-CFAR) noise estimate is formed by averaging the values of the cells in the
training area, whereas the ordered statistic constant false alarm rate
(OS-CFAR) noise estimate is formed by sorting the training area’s cell values
in descending order, and using the Nth sorted

of CA-CFAR and OS-CFAR can also be used. The AND CFAR combination performs a
logical AND of the classification outcomes of the CA-CFAR and OS-CFAR for each
CUT, while the OR CFAR combination does a logical OR.

DSP: the decision maker

When direction, speed, distance, and CFAR have
been computed, the DSP will be able to determine whether the ball thrown by a
kid from a playground and into the path of an oncoming car is likely to
intercept the vehicle in its current trajectory and whether evasive action must
be taken. In other words, the embedded system will help make the entire vehicle
safer for everyone.