Radar System Design
Chapter 13
Continuous Wave Radar
Radar System Design
Radar Types
CW systems
•CW radar
- No range information
- single target
- Unambiguous velocity
information
•FM-CW systems
- measure both range
and velocity
- broaden the transmitted
freq. spectrum
Pulsed Systems
•Pulsed radar
- measurement of range
•Pulsed Doppler radar
- measure both range
and velocity
Chapter 13: Continuous Wave Radar
13 - 1
Dr. Sheng-Chou Lin
Radar System Design
CW Radar
•Primary useful where no range information is
required
P peak
•Advantage of CW radar
P ave
Pulsed Radar Wave Shape
- Simplicity; Smaller and lighter
- Peak transmit is equal to average transmit
power  TX is lower than the peak power of a
pulsed radar; no high voltage modulators are
required for simple CW radar; radar ability to
detect targets is determined by the average
power
Rmin
- Good for short range application; pulsed radars
use TR switch or tube to protect receiver 
echo returns from short-range targets will not
reach the receiver  these targets will not be
detected. CW radars do not use TR tubes; TX/
RX isolation is achieved by using other types of
duplexer (ferrite circulators) or FM tech.
CW spectrum
fd
- It is generally simpler to extract Doppler
information for a CW system than from a pulsed
system. Pulsed radar requires additional signal
processing (gate filter, delay canceller, FFT)
Chapter 13: Continuous Wave Radar
Pulsed spectrum
fd
Isolation
13 - 2
Dr. Sheng-Chou Lin
Radar System Design
CW Radar
•Disadvantage of CW radar
- No target range formation for a simple
radar ability to determine target range is
poor
- Radar aircraft altimeter: frequency CW radars
capable of aircraft-to-terrain range
determination.
- Rather poor TX/ RX isolation
- can be overcome using proper CW
waveform design
•Common applications
- Simple (encoded), no range information:
Weapon fuses, weapon seeker,
lightweight portable personnel detector,
police radar
Chapter 13: Continuous Wave Radar
13 - 3
Dr. Sheng-Chou Lin
Radar System Design
CW Radar and Doppler Effect
CW radar as a speed monitor device
•Doppler effect (frequency shift): only indicates f d for
targets moving toward or away from radar
f d = 2v
------- , v: speed

,c = f
•General form
R
2 
v R
f d = ------------ ----- R
v
•f = 10G. v = 1mile/hour, f d = 30Hz .
Chapter 13: Continuous Wave Radar
13 - 4
Dr. Sheng-Chou Lin
Radar System Design
Simple CW Radar Systems
Homodyne receiver
•TX/RX Isolation required of circulator: power
level of the TX signal and sensitivity
- HP series 35200 lower power, solid-state, Xband, Doppler radar: 18 dB of isolation is
required
Isolation
- Circulators with 30 ~ 40 dB of isolation and
higher have also been built
- In high-power radars, more isolation may be
required
- Other isolation tech. such as dual antennas
may have to be used.
- major shortcoming  sensitivity: al low
Doppler freq. flicker noise is very strong 
amplify received signal at a high freq. 
Superheterodyne receiver
Superheterodyne receiver
•IF ~ 60 MHz 
flicker noise is negligible
•Baseband Filtering: sweeping LO + a single
filter, analog filter bank (IF stage), digital filters
or FFT processor (Baseband stage)
Chapter 13: Continuous Wave Radar
13 - 5
Dr. Sheng-Chou Lin
Radar System Design
CW Radar Doppler Ambiguity
•For infinite period of time, the received signal
(ignoring amp. fixed-phase terms):
receding approaching
s 
t = cos 
w 0 w d 
t
= cos 
wd t 
cos 
w 0 t 
wd t 
sin 
w0 t 
sin 
I
Q
–f d
•Down to baseband (Video band)
fc f d
s 
t = cos 
w d 
t = cos 
wd 
t,
1
1
S 
f = --- f
 –f d + --- f
 –f d 
2
2
•Nothing additional is done, then the sign of the
Doppler frequency shift will be lost 
Relative target motion (approaching or
receding) will be indeterminate.
–f d
fd
counter
•The problem of ambiguous relative motion IF
signal into two channels, I and Q channels.
• s 
t = cos 
wd t 
j sin 
w d t = e
j2f d t
,
f d 
S 
f = 1
--- f

, sign – for approaching
2
•Phase detection: DC output
90o
FFT
sin 
wd t 

j sin 
wd t 
= 
1
2
.
Chapter 13: Continuous Wave Radar

13 - 6
Dr. Sheng-Chou Lin
Radar System Design
CW Radar Spectrum and Resolution
Recall that we talked about
spreading of the signal
spectrum due to finite
length signals from
•Finite time in beam,
if 
; s :
B : beamwidth 
scan rate 
sec
 
t 0 B 
s
B = 2
,
 ,
s = 36sec
 t 0 2 
36 = 1 
18 sec
ex:
Bandwidth of doppler filter
BW = 18Hzsec
•Cross-section fluctuation
during time target is in
beam (effectively an amp.
modulation)
•Moving Target
components. e.g. propeller
Chapter 13: Continuous Wave Radar
13 - 7
Dr. Sheng-Chou Lin
Radar System Design
Doppler filtering
If we select the IF beamwidth so as to
encompass all possible Doppler frequencies,
the S/N will be poor. For example: ideally, we
would like to use a matched filter
•Analog approaches to optimizing
Matched Doppler filter BW
•Could also use a single tunable BP filter that
sweeps over the IF bandwidth.
•Simple digital filters
•Adaptive processing
None of these approaches by themselves
will account for sign of f d
.
•Implement at IF or RF stage.
select so that overlap occurs at -3dB
f dmin
BW
f dmax
3dB
BW IF
f IF
Chapter 13: Continuous Wave Radar
f IF
13 - 8
Dr. Sheng-Chou Lin
Radar System Design
Doppler filtering
Chapter 13: Continuous Wave Radar
13 - 9
Dr. Sheng-Chou Lin
Radar System Design
Doppler filtering and PRF
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 10
Radar System Design
CW Radar Range Equation
•S 
N = n
S
N
single
A single Pulsed SNR
PG 2 2 
SNR = ----------------------------------------3 R 4 kTBFL

4

Pt 
fr 
G 2 2 
SNR = ------------------------------------------------------3 R 4 kT 

4
1
Td 
FL
•Single pulse
•integrated over a dwell period
For CW,
- Coherent or incoherent pulsed radar
- CW Radar (~
pulse
P = P avg , B = B vid = 1 
Td
•For a single (I) channel CW  3dB loss
1
)
•P : Peak power P t . Single pulsed power = P t 

Integrated Pulses
•B: IF bandwidth, B IF 1 
 for a matched filter
Integrated Pulse SNR
• integrated SNR during a target dwell period, T d .
Tr = 1 
fr
Td
•Number of Pulses, n, during T d . n = f r T d ,
fr = 1 
Tr = PRF (Pulse repetition freq.)
B = 1
Td
•P = P avg = P t f r 
•B = B vid = 1 
Td
Chapter 13: Continuous Wave Radar
13 - 11
Dr. Sheng-Chou Lin
Radar System Design
CW Radar Maximum Range
Example: Consider a CW police radar with
single channel. Dual antenna
antenna, a circulator

a single
•P = 100mW , G = 20dB ,f = 10.525G
 = 2.85cm , F = 6dB ,L = 9dB ,
f = 1mph  f d = 30Hz = B : Velocity
,
resolution. RCS  = 30m 2 , Required SNR =
10dB.
•For CW, P = P avg = 100mW B, = 30Hz
•Max. R = 4.2 km ~ 2.6 miles
2

2.85 10 –2 
2
A e = ------- G = -------------------------------------------100
4
4
= 6.467 10 –3
S imin = F T kTB 
So 
No 
L
min
R max =
= 
–114 dBm + 10 log 
B MHz 
+ F TdB + 
So 
No 
+L
mindB
= –114 + 10 log 
30
10 –6 +
6 + 10 + 10
= –133.229dBm = 4.755 10 –14 mW
Chapter 13: Continuous Wave Radar
P t GA e 
------------------------------2S

4
imin
1
4
0.1 100 6.467 10 –3 30
= ----------------------------------------------------------------------------------2 4.755 10 –17

4
1
4
= 4010.4m = 4.01km
13 - 12
Dr. Sheng-Chou Lin
Radar System Design
CW Ranging
•In order to measure range, it is
necessary to place a time
marker (modulation) in the
transmitted signal
- amplitude, frequency,
phase
- Pulsed radar
 AM.
•CW ranging
- Frequency-modulated CW
(FMCW)
- Multiple-frequency CW
- Phase-coded-CW
•FM-CW radar
- Correlation of frequency of
TX and RX signals
- ameas
ur
eoft
ar
ge
t
’
sr
ange
and radial speed.
- Linear frequency
modulation
Chapter 13: Continuous Wave Radar
13 - 13
Dr. Sheng-Chou Lin
Radar System Design
FM-CW Ranging (No Doppler)
Frequency Modulation rate
fm = 1 

f o + f
f
Target Range
fb
fo
R = cT
------- = T = 2R
------2
c
f: Amp. of frequency modulation
f
f
We have -----b- = ---------T

4
2R f 4 8R f 8R ff m
 f b = ------- 
----------- = --------------- = --------------------c    c
c
t
T
4

1
fm = 
fb
cf b
R = ----------------8 ff m
Transmitted BW = 2 f (
Ca
r
l
s
o
n
’
sr
u
l
e
)
Maximum unambiguous range
R max
c
c
R max = --- = ---------2
2f m
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 14
Radar System Design
FM-CW Radar (Low Doppler)
(1)
f d f b
f b+
f o + f
- For positive slopes
f b-
8R ff
f b = f b+ = f b –f d = ---------------------m –f d
c
(toward)
f b = f b+ = f b –f d(negative sign)
f
fb
8R ff
f b = f b- = f b + f d = ---------------------m + f d
c
(toward)
f b = f b- = f b + f d(negative sign)
fo
t
fd = Target moving
away Radar
(away)
T
f b+ + f b8R ff
f b = ------------------ = 
f b= ---------------------m
2
c
f b- –f b+
f d = ------------------ = 2v
------2

 v = --
-
f - –f b+ 
4 b
Target moving
toward Radar
fd
(away)
- For negative slopes
c
 R = --------------------
f 
8R ff m b
fd = +

4
1
fm = 
fb
fd = +
fd = +
Target moving
toward Radar
fd = Target moving
away Radar
Chapter 13: Continuous Wave Radar
fd = -
f bf b+
13 - 15
Dr. Sheng-Chou Lin
Radar System Design
FM-CW Radar (high Doppler)
(2)
f d f b
- For positive slopes
8R ff
fb =
= f d –f b = f d –---------------------m
c
(toward)
f b = f b+ = f d –f b(negative sign)
f b+
f o + f
f b+
f
fd
f b-
fd = +
Target moving
toward Radar
fd
(away)
fb
- For negative slopes
8R ff
f b = f b- = f d + f b = ---------------------m + f d
c
(toward)
f b = f b- = f d + f b (negative sign)
fo
t
fd = Target moving
away Radar
(away)
f b- –f b+
8R ff
f b = ------------------ = 
f b= ---------------------m
2
c
c
 R = --------------------
f 
8R ff m b
f b- + f b+
2v
f d = ------------------ = ------2

 v = --
-
f - + f b+ 
4 b
T

4
fb
fd = +
fd = +
Target moving
toward Radar
fd = Target moving
away Radar
1
fm = 
fd = -
f bf b+
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 16
Radar System Design
FM-CW Range Resolution
•Range resolution (accuracy) 
R : the frequency
difference, f b , can be measured. 
f b B = 2 f
•For a linear FM, 
f b (thus R ) depends on the BW
and linearity of the modulation.
- Nonlinearity is given by
modulation from linear.
f 
B .f : deviation in
- Nonlinearity must be much less than
fm 
B .
•Maxi. range resolution 
R = c

2B  ,T( « 1 
fm
)
•For a given R max and
R 
max ,
nonlinearity
« fm 
B = R 
Rm .
EXample:
•For a range resolution of 1ft and a
maxi. unambiguous range of 3000 ft.
•the nonlinearity of the FM waveform
must be less than
R 
Rm = 1 
3000 = 0.03% .
Chapter 13: Continuous Wave Radar
13 - 17
Dr. Sheng-Chou Lin
Radar System Design
FM-CW for Multi-target
Ghost Identifying
s
n
e
iv
e
d
e
c
h
o
e
tr
a
f
s
m
it
te
r
- Adding another segment
- Adding more slopes
- Similar to Multi-PRF
R
e
c
fd
Ghost
- Multi-target (Two targets, Three targets)
- Impossible to tell the paired differences
Ghost
FFT, Filter bank
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 18
Radar System Design
FM-CW Radar Design
RF
Amplifier
TX
Modulator
VCO
(8-12G)
10dBm
Waveform
Generator
Timing signal
Velocity
Average
Frequency
counter
Range
f = 10G
f IF = 1G
Average
Frequency
counter
10dBm
Filter Bandwidth
BW = 5% ~ 50% fc
RF Sideband
Filter (fc= 9G)
IF OSC
BW = 500M
Video Amp.
RX
RF
f –f IF = 9G
Amplifier
20dB
10dBm
f IF + f b
IF
Amplifier
20dB
IF Sideband
Filter (fc= 1G)
f + fb
Chapter 13: Continuous Wave Radar
BW = 200M
13 - 19
fb
Low pass
Filter
Dr. Sheng-Chou Lin
Radar System Design
Sinusoidal-FM Ranging (1)
•Modulation with an instantaneous frequency
of f 
t = f 0 + f cos 
2f m t 
•The transmitted signal in this case is
s 
t = A 1 sin 
t


, where
t
= 2f
t d
t
T
f- sin 
= 2f o t + 
-----2f m t 
fm
•The received waveform for a point target is a replica of the transmitter waveform, in other words,
f
r 
t = A 2 sin 
t
 –T 
= A 2 sin 2f o 
t –T + ------- sin 
2f m 
t –T 

fm
•After mixing and filtering of the two signals in the receiver, the output is
sin A –sin 
A –B 
A1A2
f
r 
t s 
t = ------------ cos 2f 0 T + ------- 
sin 
2f m t –sin 
2f m 
t –T 


B
2
fm
= 2 sin B--- cos 
A –---


2
2
A1 A2
2 f
T 
= ------------ cos 2f 0 T + ----------- sin 
f m t cos 
2f 
t –---
 m  2

2
fm
•If one assume that T « 1 
f m ,
f b= 8R ff m 
c
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 20
Radar System Design
Sinusoidal-FM Ranging (2)
A1A2 
2 f
T 

r 
t s 
t = -----------2f 0 T 
cos 
----------- sin 
f m T cos 
2f 
t –---
 cos 
f m
 m  2


2 
2 f
T 

– sin 
2f 0 T 
sin 
----------- sin 
f T cos 
2f 
t –---
f
 m  2


m

A1A2 
2 f
T 
–2J cos 
+ 2 
= ------------ cos 
2f 0 T J 0 
----------- sin 
f m T 
2
2f 
t –---
J 4 
cos 

2
f

  m  2


2 
m
2 f
T 
T 
cos 
+  
–2 sin 
2f 0 T J 1 
----------- sin 
f m T 
2f m 
t –---
–J 3 cos 
2
2f 
t –---

f

 2
  m  2




m

We use expansion of the form
cos 
z cos = J o 
z +2
Bessel function

z cos 
2k
 –1 k J2k 
k=1
sin 
z cos = 2

z cos 

2k + 1 

 –1 k J2k + 1 
k=1
Chapter 13: Continuous Wave Radar
13 - 21
Dr. Sheng-Chou Lin
Radar System Design
Sinusoidal-FM Ranging (3)
If we add a Doppler component, the net result look like
= J 0 
D cos 
2f d t –0 + 2J 1 
D sin 
2f d t –0 
cos 
2f m t –m 
–2J 2 
D sin 
2f d t –0 
cos 
2
2f m t –m 

+ 2J 3 
D sin 
2f d t –0 
cos 
3
2f m t –m 
+ 
2vf
f d = -------------oc
2R
0 = 2f o 
------c 
f
D = 2
----------- sin 
f m T 
fm
0 = 2f o T
T
m = 2f m --2
f
D = 2
----------- sin 
2 f R
--- 
 mc 
fm
R
m = 2f m --c
2R
T = ------c
The harmonics of fm are modulated by the doppler frequency and weighted in amplitude
J n 
D D n R n
by a Bessel function
•Advantage: Jo gives a maximum weighting at
low D, (i.e. near range) and lower weighting at
far range (for example: far clutter)
J o 
D
J 1 
D
for a small argument
J 3 
D
J 2 
D
- When the received signals are from close-in
clutter, higher-order harmonics should be
chosen
•Disadvantages:
- Insufficient use of energy
- Probably most suitable for a single target
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 22
Radar System Design
Multiple-Frequency Ranging (1)
•Target range could be determined by measuring
the receive phase difference between the
transmitted and received waves
RX
TX
•The relative difference, , is given by
2d 4R 4fR
 c 
= ----------- = ----------- = ---------------  R = ---------- = ----------

c
4 4f

•The maximum unambiguous range
- Advantage: Large unambiguous range
= 2 R max = 
2
- Disadvantage: poor range resolution
•Two CW signals with f 1 and f 2
- 15cm at L-band (1GHz) to 1.6mm at 95 GHz
•The approach we intend to look at use two or more
CW signals that are very close-in frequency.
•If we have a sufficiently f diff = f 2 –f 1 , then
range measurement may be possible since
diff = 2 –1 is large
Transmitter signal
v 1T = sin 
2f 1 t + 1 
v 2T = sin 
2f 2 t + 2 
Receiver signal
•We examined the case of two frequency that only v
2f
 1 f D1 
t –4f 1 R 
c + 1 
1R = sin 
differed by kHz
v 2R = sin 
2f
 2 f D2 
t –4f 2 R 
c + 2 
Chapter 13: Continuous Wave Radar
13 - 23
Dr. Sheng-Chou Lin
Radar System Design
Multiple-Frequency Ranging (2)
•Low side of mixing v 1T to v 1R
v 1d = sin 
2f D1 t –4f 1 R 
c
v 2d = sin 
2f D2 t –4f 2 R 
c
•Phase difference between v 1d and v 2d
-
c2
c
R unamb = -------------- = ----------4f
2 f
f = 1.5kHz , and then
3 10 8
R unamb = ----------------------------------- = 100km
2
1.5 10 3 
- If
•However, a small f also gives a poor range
4R
 = 2f
 D1 –f D2 + ----------- 
f 1 –f 2 
resolution degree
c
- Range per (o ) degree for f = 1.5kHz
0
4R
----------- 
f 1 –f 2 
c

180 
c
R = -------------------------4f
If f 1 and f 2 are nearly the same.
3 10 8 


180 
= 
----------------------------------------------- = 278 
m

phase
41.5
 10 3 
•f = f 1 –f 2 . therefore
- If measurement accuracy is 5o, then the range
4R f
c 
resolution is 5(278) = 1.4 km
= ------------------  R = -------------c
4f
- For small f 1 –f 2 asf 1 –f 2
becomes
•Assume R = 0   = 0
smaller, R unamb becomes higher asf 1 –f 2
becomes smaller ability to determine R
Determine R necessary to give 
 = 2
- Solution: use more than 2 frequencies.
Chapter 13: Continuous Wave Radar
Dr. Sheng-Chou Lin
13 - 24
Radar System Design
Three-Frequency Ranging (3)
3-frequency system
•
f 3 –f 1 » 
f 2 –f 1 
, let f 3 –f 1 = 15kHz
·
and f 2 –f 1 = 1.5 kHz
Then by comparing phase
c 3 –1
R
f3 –f 1 = ------------------------------ = 1.91km
4f
 3 –f 1 
c 2 –1
R
f 2 –f 1 = ------------------------------ = 20.7km
4f
 2 –f 1 
•For f 3 –f 1 = 15kHz (Fine)
R unamb31 = c 
2
f3 –f 1 = 10km ,
c

180 
R = ------------------------------ = 28 
m


4f
 3 –f 1 
Infer range of
R = 2 R unamb31 + R 
f 3 –f 1 
·
= 2 10 + 1.91 = 21.91km
•For f 2 –f 1 = 1.5 kHz (Rude)
R unamb21 = c 
2
f2 –f 1 = 100km ,
c

180 
R = ------------------------------- = 278 
m


4f
 3 –f 1 
•Could use an even greater number of
frequency to obtain the best combination of
R unamb and R .
Rrude = 20.7km
•Example: Assume we are taking
measurements with an actual system and
measured values as
R fine = 21.91km
10km
3 –1 = 1.2rad , 2 –1 = 1.3rad
10km
1.91km
Chapter 13: Continuous Wave Radar
13 - 25
Dr. Sheng-Chou Lin