Overview: In this chapter we consider statistical quantities introduced in Chaps. 6-9 and adapt them to vertical and slant path propagation links. Most of the analysis presented here is for a slant path connecting a satellite in geostationary orbit and a ground or airborne platform. The uplink and downlink paths for such links are vastly different because the atmospheric turbulence layer is only near the transmitter on an uplink path and only near the receiver on a downlink path. This difference in path for the two cases leads to important differences in the derived expressions for beam spreading, scintillation index, spatial coherence radius of the wave, and the effect these parameters have on the probability of fade. In particular, we examine the effect that beam wander has on the scintillation index of an uplink path to space and its implications on fading statistics.
The greatest difference in modeling uplink/downlink paths (or general slant paths) compared with horizontal propagation paths is that in the former we need to consider changes in the refractive index structure parameter C 2 n along the path. Generally, changes in C 2 n along the path can be inferred from a profile model of C 2 n as a function of altitude. In our work here we rely on the Hufnagle-Valley C 2 n profile model, but this is not essential for the general analysis. We choose this model because it offers a little more generality than other C 2 n profile models through the use of two independent parameters identifying ground-level C 2 n values and upper atmospheric wind speeds.
Weak fluctuation theory based on the Rytov approximation is sufficient for most of the calculations required in the analysis of an uplink or downlink path provided the zenith angle is sufficiently small (less than 60 deg in most cases but may be restricted to zenith angles less than 45 deg in cases where ground-level C 2 n is large). However, it may be necessary to use strong fluctuation models for large-diameter beams in the presence of beam wander effects, and/or large zenith angles such as those that occur in near-horizon propagation paths.
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