  The Laser Interferometer Space Antenna (LISA) will detect thousands of
gravitational wave sources. Many of these sources will be overlapping in the
sense that their signals will have a non-zero cross-correlation. Such overlaps
lead to source confusion, which adversely affects how well we can extract
information about the individual sources. Here we study how source confusion
impacts parameter estimation for galactic compact binaries, with emphasis on
the effects of the number of overlaping sources, the time of observation, the
gravitational wave frequencies of the sources, and the degree of the signal
correlations. Our main findings are that the parameter resolution decays
exponentially with the number of overlapping sources, and super-exponentially
with the degree of cross-correlation. We also find that an extended mission
lifetime is key to disentangling the source confusion as the parameter
resolution for overlapping sources improves much faster than the usual square
root of the observation time.
