Signal Processing - March 2017 - 27

Table 2. Radar waveforms.
Waveform Type

Transmit Waveform s(t)

Detection Principle

Resolution

Comments

CW

e j2rfc t

Conjugate mixing

9fd = 1/T

No range information

Pulsed CW

P (Tp) e j2rfc t

Correlation

9R = cTp /2 9fd = 1/Tp

Range-Doppler performance tradeoff

Conjugate mixing

9R = c/2B 9fd = 1/PT0

Both range and Doppler information

j2r (fc + 0.5Kt) t

FMCW

e

SFCW

e j2rfn t ,

OFDM

N -1

/

n =0

,

K= B
T0

fn = fc + (n - 1) 9f

I (n) e 2r (fc +n9f) t

Inverse Fourier transform

9R = c/2B 9fd = 1/PT0

9f decides maximum range

Frequency domain
channel estimation

9R = c/N9f 9fd = 1/PTN

Suitable for vehicular communication

B denotes bandwidth of the radar. T is the amount of time for which data is captured.
N stands for a number of samples in CW and number of carriers in OFDM.
P (Tp) is rectangular pulse of duration Tp .P is number of FM/SF-CW or OFDM blocks of duration T0 and TN, respectively.
I (n) is arbitrary sequence and 9f is carrier/frequency separation in OFDM/SFCW.

radar is a major factor that affects these metrics. The radar
waveforms, as summarized in Table 2, can be characterized
whether or not they are CW, pulsed and frequency, or phase
modulated. Modulated radar waveforms include FM CW,
stepped frequency (SF) CW, orthogonal frequency-division
multiplexing (OFDM), and frequency shift keying (FSK).
Each waveform type has a certain advantage in processing,
implementation, and performance as follows:
■ In the CW radar, a conjugate mixing of a high-frequency
transmitted and received signal produces the output signal at
the Doppler frequency of the target. The resolution of frequency measurement is inversely proportional to the time
duration of the signal capture. The continuous nature of the
waveform precludes round-trip delay measurement, which is
necessary for range estimation of the target [see Figure 5(a)].

■

■

Hence, apart from ease of implementation and ability to
detect target speed, the CW radar cannot provide the
range information.
Pulsed CW radar can estimate the range information as
explained previously in the section "Basic Automotive
Radar Estimation Problems." The Doppler frequency can
be estimated by making each pulse longer and measuring
the frequency difference between the transmitted and
received pulses. As shown in Figure 5(b), the pulse duration
and pulse repetition frequency (PRF) are the key parameters in designing pulsed CW radar with desired range and
velocity resolution.
FMCW, also known as linear frequency modulation
(LFM) or chirp, is used for simultaneous range and
velocity estimation (refer to the "Velocity Estimation"

Transmitted Signal
at fc

Amplitude

Amplitude

TP
Received Signal
at fc + fd

Time
Mixer Output
at fd

CW
Radar
(a)

TPRF

Time

(b)

f2
f1

fN -1

Frequency

Frequency

fN -1

∆f

∆f
f1
f0

f0
T0

T
TN

Time

(c)

TCP

Time

(d)

Figure 5. (a) Doppler frequency measurement with the CW radar. (b) A pulsed CW radar waveform with pulse repetition time TPRF and pulsewidth Tp.
(c) An SFCW signal with period T0. (d) An OFDM block with symbols time T and cyclic prefix time TCP .
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
