Maximum detectable range using search radar equation

## Description

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

example

range = radareqsearchrng(___,Name,Value) computes the maximum detectable range 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 maximum detectable range at which a surveillance radar can detect a target.

The radar operates at a frequency of 2.5 GHz and transmits an average power of 2.1 kW. The gain of the receiving antenna is 34 decibels. Calculate the power-aperture product using these values.

lambda = freq2wavelen(2.5e9);
pav = 2100;
g = 34;
a = gain2aperture(g,lambda);
pap = pav*a;

The radar traverses a search volume with azimuths in the range [–180,180] degrees and elevations in the range [0,40] degrees. Find the solid angular search volume in steradians by using the solidangle function.

az = [-180;180];
el = [0;40];
omega = solidangle(az,el);

The antenna rotates at a rate of 12.5 RPM. Assume the system noise temperature is 487 Kelvin, the total system loss is 20 decibels, and the minimum SNR required to make a detection is 13 decibels.

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

Compute the maximum detectable range. By default, the target RCS is 1 square meter.

'Ts',ts,'Loss',loss,'unitstr','km')
R = 80.7673

## Input Arguments

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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

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 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

Radar cross section of the target, specified as a positive scalar or length-J vector of positive values. The radareqsearchrng 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

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. Units are in decibels.

Example: [10,20]

Data Types: double

Range units, specified as one of the following values:

• 'm' — Return range using meters

• 'km' — Return range using kilometers

• 'mi' — Return range using statute miles

• 'nmi' — Return range using nautical miles (US)

If you do not specify range units, then the radareqsearchrng function returns ranges using meters.

Data Types: string | char

## Output Arguments

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Maximum detectable range, returned as a scalar or a length-J column vector of positive values. Units are in meters.

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### Maximum Detectable Range Form of Search Radar Equation

The maximum detectable range form of the search radar equation, R, is:

$R={\left[\frac{{P}_{av}A{t}_{s}\sigma {F}^{2}{F}_{c}}{4\pi k{T}_{s}\left(SNR\right){L}_{a}^{2}L\Omega }\right]}^{1/4}$

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

• SNR — Required signal-to-noise ratio

• La — One-way atmospheric absorption loss

• L — Combined system losses

• Ω — Search volume in steradians

## 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.

## Version History

Introduced in R2021a