Free space path loss


L = fspl(R,lambda)


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 0, indicating no path loss.

Input Arguments


Propagation distance in meters


Wavelength in meters. The wavelength in meters is the speed of propagation divided by the frequency in hertz.

Output Arguments


Path loss in decibels. L is a nonnegative number. The minimum value of L is 0, indicating no path loss.


Calculate free space path loss in decibels incurred by a 10 gigahertz wave over a distance of 10 kilometers.

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

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Free Space Path Loss

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


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.


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

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