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Beam shape loss for Gaussian antenna pattern

Since R2021a



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.


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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 0.2π 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

More About

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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


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


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.


[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.

Extended Capabilities

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Version History

Introduced in R2021a