SNR estimate from radar equation
SNR = radareqsnr(lambda,tgtrng,Pt,tau)
SNR = radareqsnr(...,Name,Value)
the output signal-to-noise ratio (SNR) at the receiver based on the
SNR = radareqsnr(
lambda in meters, the range
meters, the peak transmit power
Pt in watts,
and the pulse width
tau in seconds.
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:
Target range in meters. When the transmitter and receiver are
colocated (monostatic radar),
Transmitter peak power in watts.
Single pulse duration in seconds.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Transmitter and receiver gain in decibels (dB). When the transmitter
and receiver are colocated (monostatic radar),
System loss in decibels (dB).
Target radar cross section in square meters. The target RCS is nonfluctuating.
System noise temperature in kelvin. The system noise temperature is the product of the effective noise temperature and the noise figure.
Default: 290 kelvin
The estimated output signal-to-noise ratio at the receiver in
Estimate the output SNR for a target with an RCS of 1 m² at a range of 50 km. The system is a monostatic radar operating at 1 GHz with a peak transmit power of 1 MW and pulse width of 0.2 μs. The transmitter and receiver gain is 20 dB. The system temperature has the default value of 290 K.
fc = 1.0e9; lambda = physconst('LightSpeed')/fc; tgtrng = 50e3; Pt = 1e6; tau = 0.2e-6; snr = radareqsnr(lambda,tgtrng,Pt,tau)
snr = 5.5868
Estimate the output SNR for a target with an RCS of 0.5 m² at 100 km. The system is a monostatic radar operating at 10 GHz with a peak transmit power of 1 MW and pulse width of 1 μs. The transmitter and receiver gain is 40 dB. The system temperature is 300 K and the loss factor is 3 dB.
fc = 10.0; T = 300.0; lambda = physconst('LightSpeed')/10e9; snr = radareqsnr(lambda,100e3,1e6,1e-6,'RCS',0.5,... 'Gain',40,'Ts',T,'Loss',3)
snr = 14.3778
Estimate the output SNR for a target with an RCS of 1 m². The radar is bistatic. The target is located 50 km from the transmitter and 75 km from the receiver. The radar operating frequency is 10.0 GHz. The transmitter has a peak transmit power of 1 MW with a gain of 40 dB. The pulse width is 1 μs. The receiver gain is 20 dB.
fc = 10.0e9; lambda = physconst('LightSpeed')/fc; tau = 1e-6; Pt = 1e6; txrvRng =[50e3 75e3]; Gain = [40 20]; snr = radareqsnr(lambda,txrvRng,Pt,tau,'Gain',Gain)
snr = 9.0547
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:
Pt — Peak transmit power in watts
Gt — Transmitter gain in decibels
Gr — 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
Rt — Range from the transmitter to the target in meters
Rr — 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 10x/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 (100/10).
The equation for the power at the input to the receiver represents the signal term in the signal-to-noise 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 Fn 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 Ts, so that Ts=TFn .
 Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.
 Skolnik, M. Introduction to Radar Systems. New York: McGraw-Hill, 1980.
 Willis, N. J. Bistatic Radar. Raleigh, NC: SciTech Publishing, 2005.
Usage notes and limitations:
Does not support variable-size inputs.