Main Content

radareqsearchpap

Power-aperture product using search radar equation

Description

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

example

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

Examples

collapse all

Compute the power-aperture product for a search radar that is required to detect a 1 square meter RCS target at a range of 111 kilometers. Assume the antenna rotates at a rate of 12.5 RPM, the signal-to-noise ratio required to make a detection is 13 decibels, the system noise temperature is 487 Kelvin, and the total system loss is 20 decibels.

range = 111e3;
tsearch = 60 / 12.5;
snr = 13;
ts = 487;
loss = 20;

The radar traverses a search volume with azimuths in the range [–180,180] degrees and elevations in the range [0,45] degrees. Find the solid angular search volume in steradians by using the solidangle function.

az = [-180;180];
el = [0;45];
omega = solidangle(az,el);

Calculate the power-aperture product. By default, the target RCS is 1 square meter.

snr = radareqsearchpap(range,snr,omega,tsearch,'Ts',ts,'Loss',loss)
snr = 2.3689e+04

Plot the power-aperture product as a function of the required SNR for a search radar system located at a range of 100 kilometers. Incorporate path loss due to absorption into the calculation of the power-aperture product.

Specify the required SNR as values in the range [–5,25] decibels. Assume the search volume is 1.5 steradians and the search time is 12 seconds.

range = 100e3;
snr = -5:25;
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 power-aperture product. By default, the target RCS is 1 square meter.

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

Plot the power-aperture product as a function of the required SNR. Before plotting, convert the power-aperture product from Wm2 to kWm2.

plot(snr,pap*0.001)
grid on
xlabel('SNR (dB)')
ylabel('Power-Aperture Product (kW\cdotm^2)')
title('Power-Aperture Product vs. SNR')

Figure contains an axes object. The axes object with title Power-Aperture Product vs. SNR contains an object of type line.

Input Arguments

collapse all

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

Required signal-to-noise ratio (SNR), specified as a scalar or a length-J vector of real values. Units are in decibels.

Example: 13

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 radareqsearchpap 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

collapse all

Power-aperture product, returned as a scalar or a length-J column vector of positive values, where J is the number of range samples. Units are in W·m2.

Data Types: double

More About

collapse all

Power-Aperture Product Form of Search Radar Equation

The power-aperture product form of the search radar equation, PavA, is:

PavA=4πΩR4kTs(SNR)La2LtsσF2Fc

where the terms of the equation are:

  • Ω — Search volume in steradians

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

  • k — Boltzmann constant

  • Ts — System temperature in Kelvin

  • SNR — Required signal-to-noise ratio

  • La — One-way atmospheric absorption loss

  • L — Combined system losses

  • 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

You can derive this equation by rearranging the SNR form of the search radar equation. See the radareqsearchsnr function for more information.

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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Introduced in R2021a