# radareqsearchpap

Power-aperture product using search radar equation

## Description

computes the available power-aperture product with additional options specified by one or
more name-value arguments. For example, `pap`

= radareqsearchpap(___,`Name,Value`

)`'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 vapour 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·m^{2}.

**Data Types: **`double`

## More About

### Power-Aperture Product Form of Search Radar Equation

The power-aperture product form of the search radar equation,
*P _{av}A*, 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*— System temperature in Kelvin_{s}*SNR*— Required signal-to-noise ratio*L*— One-way atmospheric absorption loss_{a}*L*— Combined system losses*t*— Search time in seconds_{s}*σ*— Nonfluctuating target radar cross section in square meters*F*— One-way propagation factor for the transmit and receive paths*F*— Combined range-dependent factors that contribute to the reduction of the received signal energy_{c}

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**

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