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.

Examples

Calculate Free-Space Path Loss

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

Input Arguments

R — Propagation distance of signal, in meters

real-valued 1-by-M vector | real-valued M-by-1 vector

Propagation distance of signal, in meters, specified as a real-valued 1-by-M or M-by-1 vector.

lambda — Wavelength in meters

real-valued 1-by-N vector | real-valued N-by-1 vector

Wavelength in meters, specified as a real-valued 1-by-N or N-by-1 vector. The wavelength is the speed of propagation divided by the signal frequency.

Output Arguments

L — Path loss in decibels

M-by-N non-negative matrix

Path loss in decibels, returned as a M-by-N non-negative matrix. A value of 0 signifies no path loss.

When lambda is a scalar, L has the same dimensions as R.

More About

Free Space Path Loss

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

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

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

Version History

Introduced in R2011a