Maximum detectable range using SAR equation

Since R2021a

## Syntax

``rng = radareqsarrng(lambda,snr,pt,tau,rnggain,azgain)``
``rng = radareqsarrng(lambda,snr,pt,tau,rnggain,azgain,Name,Value)``

## Description

example

````rng = radareqsarrng(lambda,snr,pt,tau,rnggain,azgain)` returns the maximum detectable range for a SAR.```

example

````rng = radareqsarrng(lambda,snr,pt,tau,rnggain,azgain,Name,Value)` specifies additional options using name-value arguments.```

## Examples

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Estimate the range for a side-looking SAR imaging a target with a radar cross-section (RCS) of 1 m${}^{2}$. The radar operates at a frequency of 5.3 GHz and has a peak power of 5 kW. The SAR uses a rectangular waveform with a pulse width of 0.05 microseconds. The antenna gain is 30 dB and the minimum detectable SNR is 30 dB. The range processing gain is 29.8 dB and the azimuth processing gain is 42.7 dB. Assume zero losses.

```lambda = freq2wavelen(5.3e9); pt = 5e3; tau = 0.05e-6; gain = 30; SNR = 30; rnggain = 29.8; azgain = 42.7; ```

Compute the maximum detectable range. Express the result in kilometers.

`rng = radareqsarrng(lambda,SNR,pt,tau,rnggain, azgain,'Gain', gain,'UnitStr','km')`
```rng = 205.6978 ```

## Input Arguments

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Wavelength of radar operating frequency in meters, specified as a positive real scalar.

Data Types: `double`

Required signal-to-noise ratio (SNR) in decibels, specified as a real scalar or a vector.

Data Types: `double`

Transmitter peak signal power in watts, specified as a positive real scalar or a vector.

Data Types: `double`

Pulse width at the antenna port in seconds, specified as a positive real scalar.

Data Types: `double`

SNR gain due to range processing in decibels, specified as a real scalar.

Data Types: `double`

SNR gain due to azimuth processing in decibels, specified as a real scalar.

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',293,'Gain',12`

Target radar cross-section in square meters, specified as a scalar or a vector. `radareqsarrng` assumes a nonfluctuating target (Swerling case 0).

Data Types: `double`

System noise temperature in kelvins, specified as a positive scalar.

Data Types: `double`

Antenna gain in decibels, specified as a scalar or 1-by-2 row vector.

• If you specify this argument as a two-element vector, the first element represents antenna transmit gain and the second element represents the antenna receive gain.

• If you specify this argument as a scalar, `radareqsarrng` assumes the antenna has equal transmit and receive gains.

Data Types: `double`

System loss in decibels, specified as a scalar or a vector.

Data Types: `double`

Custom factor in decibels, specified as a scalar or a vector. This argument contributes to the received signal energy and can include other factors.

Data Types: `double`

Unit of range length, specified as `'m'` (meter), `'km'` (kilometer), `'mi'` (statute mile), or `'nmi'` (nautical mile).

Data Types: `char` | `string`

## Output Arguments

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Maximum detectable range, returned as a column vector expressed in the units specified using `UnitStr`. For bistatic radars, each element of `rng` is the geometric mean of the range from the transmitter to the target and the range from the target to the receiver.

## Version History

Introduced in R2021a