Engee documentation

Radar Equation Calculate

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Radar Equation Calculate radar equation calculator icon - is an Engee application designed to calculate the radar basic equation for monostatic[1] and bistatic[2] radar systems.

Detailed description of the radar equation

The basic radar equation, taking into account the RMSE, is as follows:

λσ

Where:

  • - signal-to-noise ratio (SNR), shows how strong the useful signal is compared to the noise;

  • - the received signal power (W) reflected from the target;

  • - noise power (W), determines the level of background noise in the system;

  • - transmitter power (W), determines the intensity of the radiated signal;

  • - Transmit antenna gain (dimensionless value), shows how much the antenna focuses the energy in the desired direction;

  • - the gain of the receiving antenna (dimensionless value), shows how much the antenna amplifies the received signal;

  • - wavelength of the emitted signal (m), related to the radar frequency by the formula , where is the speed of light;

  • - range to target (m), shows the distance at which the object is located;

  • - total losses in the system (dimensionless value), takes into account all possible signal losses due to the atmosphere, imperfections of antennas and other factors;

  • - Boltzmann constant ( J/K), a constant used to calculate thermal noise;

  • - system noise temperature (K), determined by the temperature of the environment and the radar electronics;

  • - receiver bandwidth (Hz), determines how much of the frequency spectrum the radar receives (a wide bandwidth may allow more noise to pass through);

  • - receiver noise figure (dimensionless value), shows how much additional noise the receiver itself contributes to the signal.

Based on the formula it follows that:

  • If the transmitter power and the OSR ( ) are known, it is possible to calculate the maximum range , at which the radar is able to detect the target:

    λσπ

  • If the range and the VSL are known, it is possible to determine what transmitter power is needed for the radar to work:

    πλσ

  • If the range of and the transmitter power of are known, the expected VSWR can be calculated:

    λσπ

To open the application, go to the Engee workspace and in the upper left corner under Engee applications apps icon select Radar Equation Calculate radar equation calculator icon. The application runs in a separate browser tab and by default has the following appearance:

radar equation calculator 1

The radar equation solved by the app relates the range to the target, the transmitted power, and the signal-to-noise ratio (SNR) of the received signal. Therefore, you can use the application to:

  • Solve the problem of determining the maximum range to the target based on the radar transmit power and a given received signal VSNR;

  • Calculate the necessary transmitter power on the basis of the known range to the target and the given RMS of the received signal;

  • Calculate the value of the received signal VSD based on the known range and transmitter power.

Working with the application

Three conditional sections are used to work with the application:

radar equation calculator 5

  • Evaluated Parameter is the section where the parameter to be calculated is selected. The value of the selected parameter will be displayed in the Value of estimated parameter section. The following parameters are available for selection:

    • Range - maximum range to the target based on the radar transmitter power and the desired received ROS;

    • `Power Peak' - the power required to transmit based on the known range of the target and the desired received VSD;

    • `TIR' - value of the received TIR based on the known range and transmit power.

  • Parameters - section where parameters values are set. Each parameter is assigned a value by default, which can be changed. To the right of the value field there is a choice of measurement unit available.

    radar equation calculator 6

    The section Parameters presents all available parameters of the application with explanations.

  • Value of estimated parameter - calculated result of the radar basic equation for the parameter selected in the Estimated parameter section.

Parameters

The following is an overview of the application parameters. Their number and type depend on the selected value under Rated Parameter and on the Radar Configuration parameters (see below).

Wavelength - radar radar wavelength
`0.3 (By default).

Details

Specify the radar radar wavelength in m (by default), cm or mm.

The Wavelength is the ratio of the propagation speed of a wave to the frequency. For electromagnetic waves, the speed of propagation is equal to the speed of light.

If we denote the speed of light by , and the frequency of the wave (in hertz) by , the equation for wavelength is λ .

Pulse duration - single pulse duration
1 (By default)

Details

Specify the duration of a single pulse in µs (by default), ms or s.

Hardware losses - the sum of all signal power losses occurring in the system hardware
`0 (By default).

Details

Specify the hardware losses in dB (by default) or absolute units.

Hardware loss is a total loss factor that includes losses occurring in hardware components and propagation to and from the target.

Noise temperature - system noise temperature
`290 (By default).

Details

Specify the system noise temperature in K (by default) or °C.

The system noise temperature is the product of the system temperature and the noise figure.

Target EPR - effective scattering area (EDA) of the target
1 (By default)

Details

Specify the target EAF in м (by default), дБм .

The parameters characterise how well the object reflects radio waves back to the radar. The higher the EPR, the more visible the target is to radar, and vice versa.

The Target EPR does not change in time (does not fluctuate).

Radar Configuration - radar system type
Monostatic (by default)

Details

Specify the type of radar system:

  • Monostatic (by default) - transmitter and receiver are located in one place (monostatic radar).

  • Bistatic' - transmitter and receiver are not separated in space (bistatic radar).

Gain - transmitter and receiver gain
`20 (By default).

Details

Specify the transmitter and receiver gain in dB (by default) or absolute units.

When the transmitter and receiver are co-located (monostatic radar), the transmit and receive gains are equal.

Dependencies

This parameter is enabled only if the Radar Configuration parameters are set to Monostatic.

  • Peak power* - peak transmitter power
    `20 (By default).

Specify the peak transmitter power in kW (by default), MW, W or dBW.

Dependencies

This parameter is enabled only if the Rated Parameter is set to Range or OSH.

OCSH - minimum ratio of output signal to noise at the receiver
`10 (By default).

Details

Specify the value of OSR or calculate the OSR value using the detection specification for OSR.

You can calculate the OSD required to achieve a certain detection probability and false alarm probability using the Schnidman equation. To calculate the OSD value:

  • Click the Detection parameters for calculating the OSN section to open the advanced OSN settings:

    radar equation calculator 6

  • Enter values for the parameters Probability of correct detection, Probability of false alarm, Number of accumulation pulses, and Target EPR fluctuation model.

Dependencies

This parameter is enabled only when `Range' or `Peak Power' is set for the Reference Parameter.

Probability of correct detection -. detection probability used to estimate the RMS
`0.8102924 (by default).

Details

Specify the detection probability used to estimate the OSN using the Schnidman equation.

Dependencies

This parameter is enabled only when the Rating parameter is set to Range or Peak Power.

False alarm probability - - false alarm probability used to estimate the RMS
`0.001 (by default).

Details

Specify the false alarm probability used to estimate the OSN using the Schnidman equation.

Dependencies

This parameter is enabled only when the Reference parameter is set to Range or Peak Power.

Number of accumulation pulses - Number of accumulation pulses - Number of pulses used to estimate the RMS
1 (By default)

Details

Specify the number of pulses of incoherent radar accumulation used in the Schnidman equation to calculate the ROS.

Use multiple pulses to reduce the transmitted power while maintaining maximum target range.

Dependencies

This option is enabled only when the Reference Parameter is set to Range or Peak Power.

Target EPR fluctuation model -. the number of the Drilling case used for estimating the R.O.D.
0 (By default)

Details

Specify the Swerling model number used to estimate the OSN using the Schnidman equation:

  • 0 - uncorrelated pulses;

  • 1 - scan-to-scan decoherence. Rayleigh/exponential distribution - a series of randomly distributed scatterers with no dominant scatterer;

  • 2 - momentum-to-momentum decorrelation. Rayleigh/exponential distribution - a series of randomly distributed scatterers without a dominant scatterer;

  • 3 - scatterer-to-scatterer decorrelation. Chi-squared distribution with 4 degrees of freedom. Number of scatterers with one dominant scatterer;

  • 4 - correlation from pulse to pulse. XXi-squared distribution with 4 degrees of freedom. Multiple scatterers with one dominant.

The Swerling case numbers characterise the problem of detecting fluctuating pulses in terms of:

  • A correlation model for received pulses;

  • The distribution of scatterers affecting the probability density function (PDF) of the effective scattering area (ESA) of the target.

The Drilling examples consider all combinations of the two correlation models (scan-to-scan; pulse-to-pulse) and the two EPR LDFs (based on the presence or absence of a dominant scatterer).

Dependencies

This parameter is enabled only if the Reference parameter is set to Range or Peak Power.

  • Distance to target * target distance
    `10 (By default).

Specify the range to the target in m, km (by default), miles or nautical miles.

Dependencies

This parameter is enabled only when the Rated Parameter is set to `Peak Power' or `OSH' and the Radar Configuration parameter is set to `Monostatic'.

Range from the transmitter - range from transmitter to target
10 (By default)

Details

Specify the range from the transmitter in m, km (by default), miles or nautical miles.

If the transmitter and receiver are not in the same location (bistatic radar), specify the transmitter range separately from the receiver range.

Dependencies

This parameter is enabled only if the Rated Parameter is set to `Peak Power' or `OSH' and the Radar Configuration parameter is set to `Bistatic'.

Range from the receiver - distance from target to receiver
`10 (By default).

Details

Specify the range from the receiver in metres, kilometres (by default), miles or nautical miles.

If the transmitter and receiver are not on the same line (bistatic radar), specify the range of the receiver separately from the range of the transmitter.

Dependencies

This parameter is enabled only if the Rated Parameter is set to `Peak Power' or `OSH' and the Radar Configuration parameter is set to `Bistatic'.

Parameters in code (export from application)

The application generates code that can be used in various modelling and programming tasks, such as those described in Radar.

To do this, click the button in the upper right corner of the application radar equation calculator 2. After that in the window File browser file browser 7 a file named RadarEquationScript_YYYYYYY-MM-DD_HF:MM:SS.MSS.MSS.jl with code in Julia language will be automatically created in the window. The file will list all parameters and their values from the application at the time the button is pressed. For example:

  • Application:

    radar equation calculator 4

  • In the .jl file you created:

    # Engee code
# Generated in Engee version 25.3.
# Generated on 2025-03-24 12:22:56.919

# All values are in system units

wavelen = 0.3 # Wavelength (m)
pwidth = 1.0e-6 # Pulse duration (s)
sysloss = 0.0 # System Loss (dB)
noisetemp = 290.0 # Noise temperature (K)
rcs = 1.0 # EPR, m^2
gain = 20.0 # Antenna gain (dB)
tgtrng = 10000.0 # Range (m)
pkpow = 1000.0 # Peak transmitter power (W)
snr = radareqsnr(wavelen, tgtrng, pkpow, pwidth,
		RCS = rcs, Gain = gain,
		Loss = sysloss, Ts = noisetemp)
1. Monostatic radar system is a radar system in which the transmitter and receiver are located in the same place or very close to each other. Such radars emit a radio signal that is reflected off an object and then received by the same device.
2. Bistatic radar system is a system in which the transmitter and receiver are separated in space by a considerable distance. This allows detection of objects that may be less visible to monostatic radars, such as stealth targets. Bistatic radars are used in passive radar detection systems and can provide increased stealth and immunity to interference