Three different methods of experimental mesoscopic physics, namely, weak antilocalization effects, universal conductance fluctuations, and Aharonov-Bohm oscillations, have been used to extract the electron phase-coherence scattering rate in two-dimensional gas of InGaAs/AlInAs heterostructures. The Aharonov-Bohm oscillations reveal strong beating effects, indicating the existence of two similar periodicities of the flux dependencies. As suggested by certain theoretical models, such a behavior might be expected from the so-called Berry phase acquired by electrons with different spin orientations in the presence of strong spin-orbit coupling and Zeeman splitting. In our paper we deduce the experimental values of the dephasing length and try to compare the observed beating pattern with possible scenarios for the appearance of the Berry phase.