Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 296

variations due to scintillation. The power fluctuation, δ P , is generally modeled as

following a Nakagami-m pdf given by:

mm − 1

mP
m

δ

()

pP δ = e

− mP δ

, δ P ≥ 0 (6.52)

()

Γ

with mean value of one and variance of 1/ m . The strength of amplitude fading due to
scintillation is characterized using a parameter referred to as the S 4 index , which is
equal to the standard deviation of the power variation δ P :

1

S = (6.53)

4

m

D u e to the properties of the Nakagami-m distribution, the S 4 index cannot exceed
2.

Power fluctuations are highly correlated over short time intervals. Measured
power spectral densities of scintillation-induced power fluctuations fall off with
increasing frequency with a level proportional to f − p with p in the range of 2.5-5.5
[25]. The spectral density of the power fluctuations also tends to fall off at extremely
low frequencies (below around 0.1 Hz). Figure 6.17 shows simulated receiver power
fluctuations due to strong scintillation ( S 4 = 0.9).

Phase variations due to scintillation are most commonly modeled as following a
zero-mean Gaussian distribution:

2
2

δφ
σ φ

−

1

()

2

(6.54)

p δφ = e

2 πσ φ

with standard deviation σ φ . Phase variations are highly correlated over short periods

of time, with observed power spectral densities approximately following the form

10

5

0

− 5

− 10

− 15

− 20

− 25

− 30

− 35

− 40

5 10 15 20 25 30

Elapsed time (min)

Figure 6.17 Simulated effects of strong scintillation ( S 4 = 0.9) on received signal level.