radareqpow
Peak power estimate from radar equation
Syntax
Pt = radareqpow(lambda,tgtrng,SNR,Tau)
Pt = radareqpow(...,Name,Value)
Description
Pt = radareqpow(lambda,tgtrng,SNR,Tau) estimates
the peak transmit power required for a radar operating at a wavelength
of lambda meters to achieve the specified signaltonoise
ratio SNR in decibels for a target at a range
of tgtrng meters. The target has a nonfluctuating
radar cross section (RCS) of 1 square meter.
Pt = radareqpow(...,Name,Value) estimates
the required peak transmit power 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.

SNR 
The minimum output signaltonoise ratio at the receiver in
decibels.

Tau 
Single pulse duration in seconds.

NameValue Pair Arguments
'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' 
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 system temperature and the noise figure.
Default: 290 kelvin 
Output Arguments
Pt 
Transmitter peak power in watts.

Examples
Estimate the required peak transmit power required to achieve
a minimum SNR of 6 decibels for a target at a range of 50 kilometers.
The target has a nonfluctuating RCS of 1 square meter. The radar operating
frequency is 1 gigahertz. The pulse duration is 1 microsecond.
lambda = physconst('LightSpeed')/1e9;
tgtrng = 50e3;
tau = 1e6;
SNR = 6;
Pt = radareqpow(lambda,tgtrng,SNR,tau);
Estimate the required peak transmit power required to achieve
a minimum SNR of 10 decibels for a target with an RCS of 0.5 square
meters at a range of 50 kilometers. The radar operating frequency
is 10 gigahertz. The pulse duration is 1 microsecond. Assume a transmit
and receive gain of 30 decibels and an overall loss factor of 3 decibels.
lambda = physconst('LightSpeed')/10e9;
Pt = radareqpow(lambda,50e3,10,1e6,'RCS',0.5,...
'Gain',30,'Ts',300,'Loss',3);
Estimate the required peak transmit power for a bistatic radar
to achieve a minimum SNR of 6 decibels for a target with an RCS of
1 square meter. The target is 50 kilometers from the transmitter and
75 kilometers from the receiver. The radar operating frequency is
10 gigahertz and the pulse duration is 10 microseconds. The transmitter
and receiver gains are 40 and 20 dB respectively.
lambda = physconst('LightSpeed')/10e9;
SNR = 6;
tau = 10e6;
TxRng = 50e3; RvRng = 75e3;
TxRvRng =[TxRng RvRng];
TxGain = 40; RvGain = 20;
Gain = [TxGain RvGain];
Pt = radareqpow(lambda,TxRvRng,SNR,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 — Target's nonfluctuating
radar cross section in square meters
L — General loss factor
in decibels that accounts for both system and propagation loss
R_{t} —
Range from the transmitter to the target
R_{r} —
Range from the receiver to the target. 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. For example, the default loss factor of 0 dB results
in a loss term of 10^{0/10}=1.
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} .
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  radareqrng  radareqsnr  systemp