  Compact object binaries, mostly double with dwarfs, are believed to be a
potential source of confusion-limited noise for the Laser Interferometer Space
Antenna (LISA). In a specific frequency range, this noise may rise above the
instrumental noise sources and hence hinder detection of other types of
signals, e.g. extreme mass ratio inspirals of stellar mass objects into
supermassive black holes. In most previous studies only detached populations of
compact object binaries have been considered. Here, we investigate the
influence of Galactic populations of compact mass transferring binaries on the
shape and strength of the LISA signal and compare our results with the signal
for detached binaries only. Our population synthesis includes all binary
systems containing two compact remnants. It is found that 99.5% of these
systems are double white dwarfs, and therefore we consider only binaries
consisting of two white dwarfs when calculating the LISA signal. We find that
the mass transferring binaries contributing to the confusion limited noise
dominate the population of LISA systems by number (60%), due to their long
lifetimes (few Gyrs). However, due to the very specific physical properties of
mass transferring systems, it is found that their contribution to the noise is
negligible at low frequencies and detached systems will set the magnitude of
the confusion-limited signal in this range. However, the mass transferring
systems begin to dominate the signal at higher frequencies (f>6 mHz). The
transition frequency at which the confusion limited regime becomes important is
found at 4 mHz. The addition of mass transferring systems tends to slightly
increase the transition frequency (from 3.5 to 4 mHz).
