The complex phase method has been further extended to the problem of electr
omagnetic (EM) field scintillations on Earth-satellite GPS paths of propaga
tion. The numerical and analytic technique based on the method has been dev
eloped to characterize the transionospheric channel of propagation. The eff
ects of additional range errors due to the ionospheric electron density flu
ctuations in space and time have been studied taking into account the ray b
ending due to the inhomogeneous background ionosphere and the diffraction o
n local random ionospheric inhomogeneities. In the method developed, the im
pact of the Earth's magnetic field is accounted for by the anisotropic spat
ial spectrum of the ionospheric turbulence with different outer scales alon
g and across the magnetic field lines. The variances of the EM field phase
(yielding range errors) and level (log amplitude) fluctuations have been ca
lculated for different models of the background ionospheres characterized b
y different height electron density profiles and total electron content. Th
e conditions of the saturated regime of propagation, which will likely resu
lt in the degradation of a GPS navigation system, have been discussed. In a
ddition, the scattering function of the GPS transionospheric channel of pro
pagation has been constructed and simulated for a wideband signal.