# Documentation

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# fspl

Free space path loss

## Syntax

L = fspl(R,lambda)

## Description

L = fspl(R,lambda) returns the free space path loss in decibels for a waveform with wavelength lambda propagated over a distance of R meters. The minimum value of L is zero, indicating no path loss.

## Input Arguments

 R real-valued 1-by-M or M-by-1 vector Propagation distance of signal. Units are in meters. lambda real-valued 1-by-N or N-by-1 vector The wavelength is the speed of propagation divided by the signal frequency. Wavelength units are meters.

## Output Arguments

 L Path loss in decibels. M-by-N nonnegative matrix. A value of zero signifies no path loss. When lambda is a scalar, L has the same dimensions as R.

## Examples

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Calculate the free-space path loss (in dB) of a 10 GHz radar signal over a distance of 10 km.

fc = 10.0e9;
lambda = physconst('LightSpeed')/fc;
R = 10e3;
L = fspl(R,lambda)
L = 132.4478

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### Free Space Path Loss

The free-space path loss, L, in decibels is:

$L=20{\mathrm{log}}_{10}\left(\frac{4\pi R}{\lambda }\right)$

This formula assumes that the target is in the far-field of the transmitting element or array. In the near-field, the free-space path loss formula is not valid and can result in a loss smaller than 0 dB, equivalent to a signal gain. For this reason, the loss is set to 0 dB for range values R ≤ λ/4π.

## References

[1] Proakis, J. Digital Communications. New York: McGraw-Hill, 2001.