# beamloss

Beam shape loss for Gaussian antenna pattern

Since R2021a

## 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 = 105.0011 ```

## 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.

## References

[1] 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.

## Version History

Introduced in R2021a