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Radar Signal Processing Dr. Aamer Iqbal Bhatti Lecture 7 Radar Equation Dr. Aamer Iqbal Bhatti 1 Radar Signal Processing Dr. Aamer Iqbal Bhatti
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Lecture 7
Radar Equation
Dr. Aamer Iqbal Bhatti1
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
We have so far been talking rather loosely about detecting a
scattered pulse. Let’s now look a little more closely at the power
we can expect to be scattered back to the radar.
Suppose an isotropic radiator transmitting power PT. A target at
a distance R will receive power PR.
2
2/
4mW
R
PP T
r
An isotropic radiator is
one which radiates power
uniformly in all directions
R
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
To concentrate power in certain direction we use directed
antennas rather than isotropic radiator. i.e. antenna with gain GT
2
2/
4mW
R
GPP TT
r
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Power density incident on the target is different than the power
collected by the target.
2
2/
4mW
R
GPP TT
r
Target effective
collection area is
σ
Incident wave front
is approximately planar
at the target.
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The RCS gives the fraction of incident power that is scattered
back toward the radar. Therefore the scattered power density at
the radar is obtained by dividing by 4πR2 .
2
22/
4
1
4mW
RR
GPP TT
r
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The target scattered power collected by the receiving antenna is
PR=PrAe. Where Ae is the effective aperture of radar antenna.
2
22/
4
1
4mWA
RR
GPAPP e
TTerR
4
4
2
2
re
er
GA
or
AG
22
22/
44
1
4mW
G
RR
GPP rTT
R
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
This is the classic form of the radar range equation.
For monostatic systems a single antenna is generally used to
transmit and receive so that Gt= Gr ≡ G.
This form of the RRE is too crude to use as a design tool.
Factors have been neglected that have a significant impact on
radar performance:
Noise, System losses, Propagation behavior, Clutter,
Waveform limitations, etc.
We will discuss most of these in depth later in the course.
2
43
2
/)4(
mWR
GGPP rTT
R
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The dominant feature of the RRE is the 1/ R4 factor. Even for
targets with relatively large RCS, high transmit powers must be
used to overcome the 1/ R4 when the range becomes large.
The minimum received power that the radar receiver can "sense"
is referred to a the minimum detectable signal (MDS) and is
denoted Smin .
Given the MDS, the maximum detection range can be obtained:
41
min
3
2
max4
max
3
2
min)4()4(
S
GGPR
R
GGPSP rtTrtT
R
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Note: λ=c/f and σ = RCS. Keep λ or c, σ, and R in the same units.
On reducing the radar range equation to log form, we get.
423
2
)4( Rf
cGGPP rtTR
cRfGGPP rtTR log204log30log40log20log10log10log10log10log10
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Rewriting radar range equation.
On reducing the radar range equation to log form, we get.
RRGGPP rtTR
420
4log10
4log02log10log10log10log10
2
RRGGPP rtTR
4
4
4)(
2
One way free space loss
factor
One way free space loss
factor
Target Gain Factor
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Figure is the visualization of the path losses occurring with the
two-way radar equation given on last slide.
GGGPP rtTR log10log10log10log10
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
Receiver Sensitivity / Noise, Smin is related to the noise factors
by:
This final equation does not include system and propogation
losses.
All the losses that we want to consider will be mutiplied in the
denominator.
41
min
3
2
max)4(
S
GGPR rtT
BkTNFNSS o)()/( minmin
BkTNFR
GP
NS
o
T
)()4( 43
22
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
The SNR is
◦ Directly proportional to transmitted power.
◦ Directly proportional to RCS.
◦ Inversely proportional to the fourth power of range.
Derived equation is only valid for Point Targets.
Point Target: Point targets are those which are totally contained
within the radar’s range resolution cell.
Most microwave radars see targets as points.
Exceptions include high resolution ground mapping, diagnostic and
laser radars. These radars see their targets as area targets.
Range Resolution
Cross Range
Resolution (AZ & EL)
Radar Signal Processing
Dr. Aamer Iqbal Bhatti
There are three kinds of losses exist in radars:
◦ System Losses: Exists within the system itself.
◦ Propagation Path Losses: Losses in the medium.
◦ Ground Plane Losses: Caused by multiple signal path.
◦ LS :System Losses
◦ LA :Propagation Path Losses
◦ LGP :Ground Plane Losses
GPASI
T
LLLPR
GPSIR
43
22
)4(
