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radareqsearchsnr

Range-dependent SNR using search radar equation

Description

snr = radareqsearchsnr(range,pap,omega,tsearch) computes the available signal-to-noise ratio (SNR), snr, for a surveillance radar based on the range, range, power-aperture product, pap, solid angular search volume, omega, and search time, tsearch.

example

snr = radareqsearchsnr(___,Name,Value) computes the available SNR with additional options specified by one or more name-value arguments. For example, 'Loss',6 specifies system losses as 6 decibels.

Examples

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Compute the available signal-to-noise ratio (SNR) for a search radar at a target range of 1000 kilometers with a power-aperture product of 3×106 Wm2. Assume the search time is 10 seconds, the RCS of the target is –10 dBsm, the system noise temperature is 487 Kelvin, and the total system loss is 6 decibels.

range = 1000e3;
pap = 3e6;
tsearch = 10;
rcs = db2pow(-10);
ts = 487;       
loss = 6;

The radar surveys a region of space with azimuths in the range [0,30] degrees and elevations in the range [0,45] degrees. Find the solid angular search volume in steradians by using the solidangle function.

az = [0;30];
el = [0;45];
omega = solidangle(az,el); 

Calculate the available SNR.

snr = radareqsearchsnr(range,pap,omega,tsearch,'RCS',rcs,'Ts',ts,'Loss',loss)
snr = 13.8182

Plot the available signal-to-noise ratio (SNR) as a function of the range for a search radar with a power-aperture product of 2.5×106 Wm2. Incorporate path loss due to absorption into the calculation of the SNR.

Specify the ranges as 1000 linearly-spaced values in the interval [0,1000] kilometers. Assume the search volume is 1.5 steradians and the search time is 12 seconds.

range = linspace(1,1000e3,1000);
pap = 2.5e6;
omega = 1.5;
tsearch = 12;

Find the path loss due to atmospheric gaseous absorption by using the gaspl function. Specify the radar operating frequency as 10 GHz, the temperature as 15 degrees Celsius, the dry air pressure as 1013 hPa, and the water vapour density as 7.5 g/m3.

freq = 10e9;
temp = 15;
pressure = 1013e2;
density = 7.5;
loss = gaspl(range,freq,temp,pressure,density);

Compute the available SNR. By default, the target RCS is 1 square meter.

snr = radareqsearchsnr(range,pap,omega,tsearch,'AtmosphericLoss',loss);

Plot the SNR as a function of the range. Before plotting, convert the range from meters to kilometers.

plot(range*0.001,snr)
grid on
ylim([-10 60])
xlabel('Range (km)')
ylabel('SNR (dB)')
title('SNR vs Range')

Figure contains an axes object. The axes object with title SNR vs Range contains an object of type line.

Input Arguments

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Range, specified as a scalar or a length-J vector of positive values, where J is the number of range samples. Units are in meters.

Example: 1e5

Data Types: double

Power-aperture product, specified as a scalar or a length-J vector of positive values. Units are in W·m2.

Example: 3e6

Data Types: double

Solid angular search volume, specified as a scalar. Units are in steradians.

Given the elevation and azimuth ranges of a region, you can find the solid angular search volume by using the solidangle function.

Example: 0.3702

Data Types: double

Search time, specified as a scalar. Units are in seconds.

Example: 10

Data Types: double

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is 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 Name1,Value1,...,NameN,ValueN.

Example: 'Ts',487 specifies the system noise temperature as 487 Kelvin

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

Data Types: double

System noise temperature, specified as a positive scalar. Units are in Kelvin.

Data Types: double

System losses, specified as a scalar or a length-J vector of real values. Units are in decibels.

Example: 1

Data Types: double

One-way atmospheric absorption loss, specified as a scalar or a length-J vector of real values. Units are in decibels.

Example: [10,20]

Data Types: double

One-way propagation factor for the transmit and receive paths, specified as a scalar or a length-J vector of real values. Units are in decibels.

Example: [10,20]

Data Types: double

Custom loss factors, specified as a scalar or a length-J vector of real values. These factors contribute to the reduction of the received signal energy and can include range-dependent sensitivity time control (STC), eclipsing, and beam-dwell factors. Units are in decibels.

Example: [10,20]

Data Types: double

Output Arguments

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Available signal-to-noise ratio, returned as a scalar or a length-J column vector of real values, where J is the number of range samples. Units are in decibels.

More About

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SNR Form of Search Radar Equation

The signal-to-noise ratio form of the search radar equation, SNR, is:

SNR=PavAtsσF2Fc4πkTsR4La2LΩ

where the terms of the equation are:

  • Pav — Average transmit power in watts

  • A — Antenna effective aperture in square meters

  • ts — Search time in seconds

  • σ — Nonfluctuating target radar cross section in square meters

  • F — One-way propagation factor for the transmit and receive paths

  • Fc — Combined range-dependent factors that contribute to the reduction of the received signal energy

  • k — Boltzmann constant

  • Ts — System temperature in Kelvin

  • R — Target range in meters. The equation assumes the radar is monostatic.

  • La — One-way atmospheric absorption loss

  • L — Combined system losses

  • Ω — Search volume in steradians

You can derive this equation based on assumptions about the SNR form of the standard radar equation. For more information about the SNR form of the standard radar equation, see the radareqsnr function. These are the assumptions:

  • The radar is monostatic, so that R = Rt = Rr, where Rt is the range from the transmitter to the target and Rr is the range from the receiver to the target.

  • The search time is the time the transmit beam takes to scan the entire search volume. As a result, you can express the search time, ts, in terms of the search volume, Ω, the area of the beam in steradians, Ωt, and the dwell time in seconds, Td.

    ts=TdΩΩt

  • The transmit antenna beam has an ideal rectangular shape. As a result, you can express the transmit antenna gain, Gt, in terms of the angular area of the antenna beam.

    Gt=4πΩt

  • The receive antenna is ideal. This means you can express the receive antenna gain, Gr, in terms of the antenna effective aperture, A, and the radar operating frequency wavelength, λ.

    Gr=4πAλ2

References

[1] Barton, David Knox. Radar Equations for Modern Radar. Artech House Radar Series. Boston, Mass: Artech House, 2013.

[2] Skolnik, Merrill I. Introduction to Radar Systems. Third edition. McGraw-Hill Electrical Engineering Series. Boston, Mass. Burr Ridge, IL Dubuque, IA: McGraw Hill, 2001.

Extended Capabilities

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