radareqpow
Description
estimates the peak transmit power, Pt
= radareqpow(lambda
,tgtrng
,SNR
,tau
)Pt
, required for a radar operating
at a wavelength of lambda
meters to achieve the specified
signal-to-noise ratio, SNR
, in decibels for a target at a range of
tgtrng
meters. tau
is the pulse width. The
target has a nonfluctuating radar cross section (RCS) of 1 square meter.
Examples
Compute Required Transmit Power
Estimate the required peak transmit power required to achieve a minimum SNR of 6 dB for a target at a range of 50 km. The target has a nonfluctuating RCS of 1 m². The radar operating frequency is 1 GHz. The pulse duration is 1 μs.
fc = 1.0e9;
lambda = physconst('LightSpeed')/fc;
tgtrng = 50e3;
tau = 1e-6;
SNR = 6;
Pt = radareqpow(lambda,tgtrng,SNR,tau)
Pt = 2.1996e+05
Compute Required Transmit Power at Specified System Temperature
Estimate the required peak transmit power required to achieve a minimum SNR of 10 dB for a target with an RCS of 0.5 m² at a range of 50 km. The radar operating frequency is 10 GHz. The pulse duration is 1 μs. Assume a transmit and receive gain of 30 dB and an overall loss factor of 3 dB. The system temperature is 300 K.
fc = 10.0e9; lambda = physconst('LightSpeed')/fc; Pt = radareqpow(lambda,50e3,10,1e-6,'RCS',0.5, ... 'Gain',30,'Ts',300,'Loss',3)
Pt = 2.2809e+06
Compute Required Transmit Power for Bistatic Radar
Estimate the required peak transmit power for a bistatic radar to achieve a minimum SNR of 6 dB for a target with an RCS of 1 m². The target is 50 km from the transmitter and 75 km from the receiver. The radar operating frequency is 10 GHz and the pulse duration is 10 μs. The transmitter and receiver gains are 40 dB and 20 dB, respectively.
fc = 10.0e9; lambda = physconst('LightSpeed')/fc; SNR = 6; tau = 10e-6; TxRng = 50e3; RvRng = 75e3; TxRvRng =[TxRng RvRng]; TxGain = 40; RvGain = 20; Gain = [TxGain RvGain]; Pt = radareqpow(lambda,TxRvRng,SNR,tau,'Gain',Gain)
Pt = 4.9492e+04
Input Arguments
lambda
— Wavelength of radar operating frequency
positive scalar
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:
Data Types: double
tgtrng
— Target range
positive scalar | two-element row vector of positive values | length-J column vector of positive values | J-by-2 matrix of positive values
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 oftgtrng
has the form[TxRng RxRng]
, whereTxRng
is the range from the transmitter to the target andRxRng
is the range from the receiver to the target.
Units are in meters.
Data Types: double
SNR
— Input signal-to-noise ratio at receiver
scalar | length-J real-valued vector
Input signal-to-noise ratio (SNR) at the receiver, specified as a scalar or length-J real-valued vector. J is the number of targets. Units are in dB.
Data Types: double
tau
— Single pulse duration
positive scalar
Single pulse duration, specified as a positive scalar. Units are in seconds.
Data Types: double
Name-Value Arguments
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',3.0
RCS
— Radar cross section
1
(default) | positive scalar | length-J vector of positive values
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
Ts
— System noise temperature
290
(default) | positive scalar
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
Gain
— Transmitter and receiver gains
20
(default) | scalar | real-valued 1-by-2 row vector
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
Loss
— System losses
0
(default) | scalar | length-J real-valued vector
System losses, specified as a scalar. Units are in dB.
Example: 1
Data Types: double
AtmosphericLoss
— Atmospheric absorption loss
0 (default) | scalar | two-element row vector of real values | length-J column vector of real values | J-by-2 matrix of real values
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
PropagationFactor
— Propagation factor
0 (default) | scalar | two-element row vector of real values | length-J column vector of real values | J-by-2 matrix of real values
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
CustomFactor
— Custom factor
0 (default) | scalar | length-J column vector of real values
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
Pt
— Transmitter peak power
positive scalar
Transmitter peak power, returned as positive scalar. Units are in watts.
More About
Point Target Radar Range Equation
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 — Transmit antenna gain
Gr — Receive antenna gain. If the radar is monostatic, the transmit and receive antenna gains are identical.
λ — Radar 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
Rt — Range from the transmitter to the target
Rr — 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 10x/10 where x denotes the variable. For example, the default loss factor of 0 dB results in a loss term of 100/10=1.
Receiver Output Noise Power
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. This value is denoted by Ts, so that Ts=TFn .
Receiver Output SNR
Define the output SNR. The receiver output SNR is:
You can derive this expression using the following equations:
Received signal power in Point Target Radar Range Equation
Output noise power in Receiver Output Noise Power
Theoretical Maximum Detectable Range
Compute the maximum detectable range of a target.
For monostatic radars, the range from the target to the transmitter and receiver is identical. Denoting this range by R, you can express this relationship as .
Solving for R
For bistatic radars, the theoretical maximum detectable range is the geometric mean of the ranges from the target to the transmitter and receiver:
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
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Does not support variable-size inputs.
Version History
Introduced in R2021a
See Also
phased.Transmitter
| phased.ReceiverPreamp
| noisepow
| radareqrng
| radareqsnr
| systemp
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