  The ESA's Mars Express solar corona experiments were performed at two solar
conjunctions in the years 2015 and 2017 by a number of radio telescopes in the
European VLBI Network. This paper presents the methods to measure the frequency
and phase fluctuations of the spacecraft radio signal, and the applications to
study the characteristics of the plasma turbulence effects on the signal at a
single station and at multiple stations via cross-correlation. The power
spectra of the frequency fluctuations observed between 4.9 and 76.3 $\rm R_{s}$
have a power-law shape close to a Kolmogorov spectrum over the frequency
interval $ \nu_{lo}< \nu <\nu_{up}$, where the nominal value of $\nu_{lo}$ is
set to 3 mHz and $\nu_{up}$ is in the range of 0.03 $\sim$ 0.15 Hz. The RMS of
the frequency fluctuations is presented as a function of the heliocentric
distance. Furthermore, we analyse the variations of the electron column density
fluctuations at solar offsets 4.9 $\rm{R_{s}}$ and 9.9 $\rm{R_{s}}$ and the
cross-correlation products between the VLBI stations. The power density of the
differential fluctuations between different stations decreases at $\nu < 0.01$
Hz. Finally, the fast flow speeds of solar wind $>700$ $\rm{km~s^{-1}}$ are
derived from the cross-correlation of frequency fluctuations at $\nu < 0.01$
Hz. The fast flow speeds of solar wind correspond to the high heliolatitude of
the coronal region that the radio rays passed. The VLBI observations and
analysis methods can be used to study the electron column density fluctuations
and the turbulence at multiple spatial points in the inner solar wind by
providing multiple lines of sight between the Earth and the spacecraft.
