radareqsearchpap

Power-aperture product using search radar equation

Since R2021a

Syntax

pap = radareqsearchpap(range,snr,omega,tsearch)

pap = radareqsearchpap(___,Name,Value)

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.

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

Compute Power-Aperture Product Using Search Radar Equation

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 Power-Aperture Product as Function of Required SNR

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 vapor density as 7.5 $\mathrm{g}/{\mathrm{m}}^3$.

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 $\mathrm{W}\cdot {\mathrm{m}}^2$ to $\mathrm{kW}\cdot {\mathrm{m}}^2$.

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

Input Arguments

range — Range

scalar | length-J vector of positive values

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

snr — Required signal-to-noise ratio

scalar | length-J vector of real values

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

omega — Solid angular search volume

scalar

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

tsearch — Search time

scalar

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

Example: 10

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

RCS — Radar cross section

1 (default) | positive scalar | length-J vector of positive values

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

Ts — System noise temperature

290 (default) | positive scalar

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

Data Types: double

Loss — System losses

0 (default) | scalar | length-J vector of real values

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

Example: 1

Data Types: double

AtmosphericLoss — One-way atmospheric absorption loss

0 (default) | scalar | length-J vector of real values

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

PropagationFactor — One-way propagation factor

0 (default) | scalar | length-J vector of real values

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

CustomFactor — Custom loss factors

0 (default) | scalar | length-J vector of real values

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

pap — Power-aperture product

scalar | length-J column vector of positive values

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

Power-Aperture Product Form of Search Radar Equation

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

$$P_{av}A=\frac{4\pi \Omega R^{4}k{T}_s(SNR)L_a^{2}L}{t_s\sigma F^2{F}_c}$$

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

• T_s — System temperature in Kelvin

• SNR — Required signal-to-noise ratio

• L_a — One-way atmospheric absorption loss

• L — Combined system losses

• t_s — Search time in seconds

• σ — Nonfluctuating target radar cross section in square meters

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

• F_c — 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™.

Version History

Introduced in R2021a