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radareqsnr

SNR estimate from radar equation

Since R2021a

Description

SNR = radareqsnr(lambda,tgtrng,Pt,tau) estimates the output signal-to-noise ratio, SNR, at the receiver based on the wavelength lambda, the range tgtrng, the peak transmit power Pt, and the pulse width tau.

example

SNR = radareqsnr(lambda,tgtrng,Pt,tau,Name,Value) estimates the output SNR at the receiver with additional options specified by one or more Name,Value pair arguments.

example

Examples

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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

Input Arguments

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Wavelength of radar operating frequency, specified as a positive scalar. The wavelength is the ratio of the wave propagation speed to frequency. Units are in meters. 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:

λ=cf

Data Types: double

Target ranges for a monostatic or bistatic radar.

  • Monostatic radar - the transmitter and receiver are co-located. tgtrng is a real-valued positive scalar or length-J real-valued positive column vector. J is the number of targets.

  • Bistatic radar - the transmitter and receiver are separated. tgtrng is a 1-by-2 row vector with real-valued positive elements or a J-by-2 matrix with real-valued positive elements. J is the number of targets. Each row of tgtrng has the form [TxRng RxRng], where TxRng is the range from the transmitter to the target and RxRng is the range from the receiver to the target.

Units are in meters.

Data Types: double

Transmitter peak power, specified as a positive scalar. Units are in watts.

Data Types: double

Single pulse duration, in the case of a rectangular pulse; more generally, tau is the reciprocal of the waveform bandwidth. Specified as a positive scalar. Units are in seconds.

Data Types: double

Single pulse duration, specified as a positive scalar. Units are in seconds.

Data Types: double

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'RCS',5.0,'Ts',295

Radar cross section specified as a positive scalar or length-J vector of positive values. J is the number of targets. The target RCS is nonfluctuating (Swerling case 0). Units are in square meters.

Data Types: double

System noise temperature, specified as a positive scalar. The system noise temperature is the product of the system temperature and the noise figure. Units are in Kelvin.

Data Types: double

Transmitter and receiver gains, specified as a scalar or real-valued 1-by-2 row vector. When the transmitter and receiver are co-located (monostatic radar), Gain is a real-valued scalar. Then, the transmit and receive gains are equal. When the transmitter and receiver are not co-located (bistatic radar), Gain is a 1-by-2 row vector with real-valued elements. If Gain is a two-element row vector it has the form [TxGain RxGain] representing the transmit antenna and receive antenna gains. Units are in dB.

Example: [15,10]

Data Types: double

System losses, specified as a scalar. Units are in dB.

Example: 1

Data Types: double

Atmospheric absorption losses for the transmit and receive paths.

  • When the absorption is a scalar or length-J column vector, the loss specifies the atmospheric absorption loss for a one-way path.

  • When the absorption is a 1-by-2 row vector or J-by-2 column vector, the first column specifies the atmospheric absorption loss for the transmit path and the second column of contains the atmospheric absorption loss for the receive path

Example: [10,20]

Data Types: double

Propagation factor for the transmit and receive paths.

  • When the propagation factor is a scalar or length-J column vector, the propagation factor is specified for a one-way path.

  • When the propagation factor is a 1-by-2 row vector or J-by-2 column vector, the first column specifies the propagation factor for the transmit path and the second column of contains the propagation factor for the receive path

Units are in dB.

Example: [10,20]

Data Types: double

Custom loss factors specified as a scalar or length-J column vector of real values. J is the number of targets. These factors contribute to the reduction of the received signal energy and can include range-dependent Sensitive Time Control (STC), eclipsing, and beam-dwell factors. Units are in dB.

Example: [10,20]

Data Types: double

Output Arguments

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Minimum output signal-to-noise ratio at the receiver, returned as a scalar. Units are in dB.

Data Types: double

More About

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References

[1] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.

[2] Skolnik, M. Introduction to Radar Systems. New York: McGraw-Hill, 1980.

[3] Willis, N. J. Bistatic Radar. Raleigh, NC: SciTech Publishing, 2005.

Extended Capabilities

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Version History

Introduced in R2021a