Global Positioning System Reference
In-Depth Information
C.3
Conversion Between PSDs and PFDs
While PFDs arise often in documents involving spectrum protection and radio fre-
quency interference, most signal theory is written in terms of PSDs. This section
describes how to convert between the two quantities.
Recall that a PFD describes the power per unit area (often a square meter) nor-
mal to a propagating electromagnetic wave, while a PSD describes the power per
bandwidth (often 1 Hz, but sometime 1 kHz, 4 kHz, or 1 MHz) in a signal. These
are very different concepts and quantities, and conversion between them requires an
intermediate quantity—power—as well as definition of the receive antenna's effec-
tive area and of the normalized (unit power) PSD for the unit-power signal, in units
of seconds (or reciprocal hertz).
To convert from PFD to PSD, first use (C.5) and the given effective area of the
receive antenna. Often, a unity-gain antenna is assumed. Note from (C.3) that at
c
4
frequencies greater than
84 3
.
MHz, the effective area of a unity-gain
π
antenna is less than unity, so for calculations involving GNSS, the effective area is
typically negative when expressed in decibels. The result is power, in units of watts.
Multiply the power by the normalized (unit area) PSD to obtain the actual PSD in
units of W/Hz. To find the PSD in a given bandwidth centered at a given center fre-
quency, merely integrate the actual PSD over that bandwidth at that frequency. In
many cases, the latter step can be approximated by evaluating the PSD at the center
frequency and then multiplying it by the bandwidth. As long as the actual PSD is
well approximated by a straight (not necessarily horizontal) line over the given
bandwidth, the result is valid.
To convert from PSD to PFD, integrate the PSD over all frequencies to deter-
mine the total power. Then, using (C.5), divide the total power by the effective area
of the receive antenna (for frequencies of typical interest in GNSS, this involves add-
ing a positive quantity in decibels) to obtain the PFD.
References
[1]
Parsons, J. D., The Mobile Radio Propagation Channel , 2nd ed., New York: John Wiley
and Sons, 2000.
[2]
Friis, H. T., “A Note on a Simple Transmission Formula,” Proc. IRE , Vol. 34, 1946,
pp. 254-256.
 
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