# beamloss

Beam shape loss for Gaussian antenna pattern

## Syntax

``lb = beamloss``
``lb = beamloss(is2d)``

## Description

example

````lb = beamloss` calculates the beam shape loss `lb` for a radar that scans over one angular dimension (1-D). The `beamloss` function assumes the antenna has a Gaussian pattern and densely samples the angular domain. For the angular domain to be densely sampled, beam dwells must be spaced by less than 0.71 of the one-way half-power beamwidth.You can use `lb` as an accurate approximation of loss for antenna patterns other than Gaussian patterns.```
````lb = beamloss(is2d)`, where `is2d` is `1` (`true`), calculates the beam shape loss for a scanning radar over two angular dimensions (2-D). The default for `is2d` is `0` (`false`), which calculates the beam shape loss for a scanning radar in one angular dimension.```

## Examples

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Calculate the power-aperture product for a search radar performing a two-dimensional search by using the `radareqsearchpap` function. Include beam shape loss by using the `beamloss` function.

Specify a search volume of `0.2`$\pi$ steradians and a search time of `4` seconds. The radar requires a signal-to-noise ratio (SNR) of `20` decibels to detect a 1 square meter radar cross-section (RCS) target at a range of `100000` meters. By default, the system noise temperature is 290 kelvin.

```omega = 0.2*pi; tsearch = 4; snr = 20; range = 100000;```

Calculate the power-aperture product, including the beam shape loss. Assume the rest of the losses for the system are 0 decibels.

```lb = beamloss; pap = radareqsearchpap(range,snr,omega,tsearch,'Loss',lb)```
```pap = 105.0012 ```

## Input Arguments

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Scanning in two angular dimensions, specified as numeric or logical `1` (`true`) or `0` (`false`). When you do not specify `is2d`, or specify `is2d` as `0` (`false`), the function assumes the radar scans in one angular dimension.

Data Types: `logical`

## Output Arguments

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Beam shape loss in decibels, returned as a scalar.

Data Types: `double`

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### Beam-Shape Loss

Incorporate beam shape loss into the standard form of the radar range equation implemented by the `radareqsearchsnr`, `radareqsearchrng`, and `radareqsearchpap` functions to account for the use of peak gain instead of effective gain. The effective gain results from the two-way pattern of the scanning antenna modulating the received train of pulses.

The power equation for 1-D beam shape loss for an antenna with a Gaussian pattern, Lp1, is

`${L}_{p1}=\sqrt{\frac{8\mathrm{ln}2}{\pi }}=1.3288$`

The power equation for 2-D beam shape loss for an antenna with a Gaussian pattern, Lp2, is

`${L}_{p1}=\frac{8\mathrm{ln}2}{\pi }=1.7658$`

In decibels, the 1-D beam shape loss is 1.2338 and the 2-D beam shape loss is 2.4677.

You can use beam shape loss for an antenna with a Gaussian pattern as an accurate approximation of loss for antennas with other patterns.

 Barton, David Knox. "Beamshape Loss for Different Patterns." In Radar Equations for Modern Radar, 148–149. Artech House Radar Series. Boston, Mass: Artech House, 2013. 