  We analyze the origin of the parabolic background of magnetoresistance
oscillations measured in finite-width superconducting mesoscopic rings with
input and output stubs and in patterned films. The transmission model
explaining the sinusoidal oscillation of magnetoresistance is extended to
address the parabolic background as a function of the magnetic field. Apart
from the interference mechanism activated by the ring, pinned superconducting
vortices as topological defects introduce a further interference-based
distribution of supercurrents that affects, in turn, the voltmeter-sensed
quasiparticles. The onset of vortices changes the topology of the
superconducting state in a mesoscopic ring in a such a way that the full
magnetoresistance dynamics can be interpreted owing to the interference of the
constituents of the order parameter induced by both the ring with its
doubly-connected topology and the vortex lattice in it.
