radareqsnr
SNR estimate from radar equation
Syntax
SNR = radareqsnr(lambda,tgtrng,Pt,tau)
SNR = radareqsnr(...,Name,Value)
Description
SNR = radareqsnr(lambda,tgtrng,Pt,tau) estimates
the output signaltonoise ratio (SNR) at the receiver based on the
wavelength lambda in meters, the range tgtrng in
meters, the peak transmit power Pt in watts,
and the pulse width tau in seconds.
SNR = radareqsnr(...,Name,Value) estimates
the output SNR at the receiver with additional options specified by
one or more Name,Value pair arguments.
lambda 
Wavelength of radar operating frequency in meters. The wavelength
is the ratio of the wave propagation speed to frequency. For electromagnetic
waves, the speed of propagation is the speed of light. Denoting the
speed of light by c and the frequency in hertz
of the wave by f, the equation for wavelength is:

tgtrng 
Target range in meters. When the transmitter and receiver are
colocated (monostatic radar), tgtrng is a realvalued
positive scalar. When the transmitter and receiver are not colocated
(bistatic radar), tgtrng is a 1by2 row vector
with realvalued positive elements. The first element is the target
range from the transmitter, and the second element is the target range
from the receiver.

Pt 
Transmitter peak power in watts.

tau 
Single pulse duration in seconds.

NameValue Pair Arguments
Specify optional commaseparated pairs of Name,Value arguments.
Name is the argument
name and Value is the corresponding
value. Name must appear
inside single quotes (' ').
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN.
'Gain' 
Transmitter and receiver gain in decibels (dB). When the transmitter
and receiver are colocated (monostatic radar), Gain is
a realvalued scalar. The transmit and receive gains are equal. When
the transmitter and receiver are not colocated (bistatic radar), Gain is
a 1by2 row vector with realvalued elements. The first element is
the transmitter gain, and the second element is the receiver gain.
Default: 20 
'Loss' 
System loss in decibels (dB). Loss represents
a general loss factor that comprises losses incurred in the system
components and in the propagation to and from the target.
Default: 0 
'RCS' 
Target radar cross section in square meters. The target RCS
is nonfluctuating.
Default: 1 
'Ts' 
System noise temperature in kelvin. The system noise temperature
is the product of the effective noise temperature and the noise figure.
Default: 290 kelvin 
Output Arguments
SNR 
The estimated output signaltonoise ratio at the receiver in
decibels. SNR is 10log_{10}(P_{r}/N).
The ratio P_{r}/N is
defined in Receiver Output SNR.

Examples
Estimate the output SNR for a target with an RCS of 1 square
meter at a range of 50 kilometers. The system is a monostatic radar
operating at 1 gigahertz with a peak transmit power of 1 megawatt
and pulse width of 0.2 microseconds. The transmitter and receiver
gain is 20 decibels and the system temperature is 290 kelvin.
lambda = physconst('LightSpeed')/1e9;
tgtrng = 50e3;
Pt = 1e6;
tau = 0.2e6;
snr = radareqsnr(lambda,tgtrng,Pt,tau);
Estimate the output SNR for a target with an RCS of 0.5 square
meters at 100 kilometers. The system is a monostatic radar operating
at 10 gigahertz with a peak transmit power of 1 megawatt and pulse
width of 1 microsecond. The transmitter and receiver gain is 40 decibels.
The system temperature is 300 kelvin and the loss factor is 3 decibels.
lambda = physconst('LightSpeed')/10e9;
snr = radareqsnr(lambda,100e3,1e6,1e6,'RCS',0.5,...
'Gain',40,'Ts',300,'Loss',3);
Estimate the output SNR for a target with an RCS of 1 square
meter. The radar is bistatic. The target is located 50 kilometers
from the transmitter and 75 kilometers from the receiver. The radar
operating frequency is 10 gigahertz. The transmitter has a peak transmit
power of 1 megawatt with a gain of 40 decibels. The pulse width is
1 microsecond. The receiver gain is 20 decibels.
lambda = physconst('LightSpeed')/10e9;
tau = 1e6;
Pt = 1e6;
txrvRng =[50e3 75e3];
Gain = [40 20];
snr = radareqsnr(lambda,txrvRng,Pt,tau,'Gain',Gain);
More About
expand all
The point target radar range equation estimates the power at
the input to the receiver for a target of a given radar cross section
at a specified range. The model is deterministic and assumes isotropic
radiators. The equation for the power at the input to the receiver
is
where the terms in the equation are:
P_{t} —
Peak transmit power in watts
G_{t} —
Transmitter gain in decibels
G_{r} —
Receiver gain in decibels. If the radar is monostatic, the transmitter
and receiver gains are identical.
λ — Radar operating
frequency wavelength in meters
σ — Nonfluctuating
target radar cross section in square meters
L — General loss factor
in decibels that accounts for both system and propagation losses
R_{t} —
Range from the transmitter to the target in meters
R_{r} —
Range from the receiver to the target in meters. If the radar is monostatic,
the transmitter and receiver ranges are identical.
Terms expressed in decibels such as the loss and gain factors
enter the equation in the form 10^{x/10} where x denotes
the variable value in decibels. For example, the default loss factor
of 0 dB results in a loss term equal to one in the equation (10^{0/10}).
The equation for the power at the input to the receiver represents
the signal term in the signaltonoise ratio. To model the noise term,
assume the thermal noise in the receiver has a white noise power spectral
density (PSD) given by:
where k is the
Boltzmann constant and T is the effective noise
temperature. The receiver acts as a filter to shape the white noise
PSD. Assume that the magnitude squared receiver frequency response
approximates a rectangular filter with bandwidth equal to the reciprocal
of the pulse duration, 1/τ. The total noise
power at the output of the receiver is:
where F_{n} is
the receiver noise factor.
The product of the effective noise temperature and the receiver
noise factor is referred to as the system temperature and
is denoted by T_{s}, so that T_{s}=TF_{n} .
The receiver output SNR is:
You can derive this expression using the following equations:
References
[1] Richards, M. A. Fundamentals of Radar Signal
Processing. New York: McGrawHill, 2005.
[2] Skolnik, M. Introduction to Radar Systems.
New York: McGrawHill, 1980.
[3] Willis, N. J. Bistatic Radar.
Raleigh, NC: SciTech Publishing, 2005.
See Also
noisepow  phased.ReceiverPreamp  phased.Transmitter  radareqpow  radareqrng  systemp