Global Positioning System Reference
In-Depth Information
APPENDIX C
Free-Space Propagation Loss
John W. Betz
The MITRE Corporation
C.1
Introduction
Calculating propagation loss is a fundamental tool in systems engineering for
GNSS, since this loss relates the power at a source (e.g., a satellite transmitter or an
interferer) to the power at a destination (e.g., a GNSS receiver). The propagation
loss typically depends on the distance between source and destination, as well other
factors.
The simplest common expression for propagation loss is called free-space prop-
agation loss , since it applies in free space (source and receiver are located in a vac-
uum or equivalent, with no other objects in the vicinity). Although this expression is
often employed, there are widespread misunderstandings of its applicability (under
what conditions does it apply?) and its technical characteristics (e.g., in what sense
is free-space propagation loss frequency dependent?).
Entire texts (e.g., [1]) are devoted to radio wave propagation—predicting, mea-
suring, and compensating for its effects. This appendix only touches on one simple
and common model for radio wave propagation—free-space propagation loss. It
also addresses a related topic—how to convert back and forth between power flux
densities (PFDs) and power spectral densities (PSDs).
C.2
Free-Space Propagation Loss
Propagation loss is defined as the ratio of the power transmitted in the direction of
the receive antenna to the power at the terminals of a receive antenna, for a
unity-gain receive antenna. If the receive antenna has gain other than unity, the
received power is divided by the receive antenna gain in taking this ratio. The trans-
mit antenna actually radiates P T watts, and has a gain of G T (dimensionless), pro-
ducing an EIRP of P T G T watts. The receive antenna has a gain of G R . The power at
the receive antenna terminals is denoted P R , so that the propagation loss is the
dimensionless quantity
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