Maximum theoretical range estimate
Estimate Maximum Detectable Range
Estimate the theoretical maximum detectable range for a monostatic radar operating at 10 GHz using a pulse duration of 10 μs. Assume the output SNR of the receiver is 6 dB.
lambda = physconst('LightSpeed')/10e9; SNR = 6; tau = 10e-6; Pt = 1e6; maxrng = radareqrng(lambda,SNR,Pt,tau)
maxrng = 4.1057e+04
Estimate Maximum Detectable Range With Target RCS
Estimate the theoretical maximum detectable range for a monostatic radar operating at 10 GHz using a pulse duration of 10 μs. The target RCS is 0.1 m². Assume the output SNR of the receiver is 6 dB. The transmitter-receiver gain is 40 dB. Assume a loss factor of 3 dB.
lambda = physconst('LightSpeed')/10e9; SNR = 6; tau = 10e-6; Pt = 1e6; RCS = 0.1; Gain = 40; Loss = 3; maxrng2 = radareqrng(lambda,SNR,Pt,tau,'Gain',Gain, ... 'RCS',RCS,'Loss',Loss)
maxrng2 = 1.9426e+05
lambda — Wavelength of radar operating frequency
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:
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.
Pt — Transmitted peak power
Transmitter peak power, specified as a positive scalar. Units are in watts.
tau — Single pulse duration
Single pulse duration, specified as a positive scalar. Units are in seconds.
Specify optional pairs of arguments as
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.
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.
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.
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
Loss — System losses
0 (default) | scalar | length-J real-valued vector
System losses, specified as a scalar. Units are in dB.
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 STC, eclipsing, and beam-dwell factors. Units are in dB.
unitstr — Units of the estimated maximum theoretical range
'm' (default) |
Units of the estimated maximum theoretical range, specified as one of:
'nmi'nautical miles (U.S.)
maxrng — Estimated theoretical maximum detectable range
The estimated theoretical maximum detectable range, returned as a positive scalar.
The units of
maxrng are specified by
For bistatic radars,
maxrng is the geometric mean of the range from
the transmitter to the target and the receiver to the target.
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:
 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.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Does not support variable-size inputs.
Introduced in R2021a