  We discuss spatial fluctuations in the gravitational wave background arising
from unresolved Galactic binary sources, such as close white dwarf binaries,
due to the fact the galactic binary source distribution is anisotropic. We
introduce a correlation analysis of the two data streams of the Laser
Interferometer Space Antenna (LISA) to extract spherical harmonic coefficients,
in an independent manner, of the hexadecapole moment ($l=4$) related to the
projected two-dimensional density distribution of the binary source population.
The proposed technique complements and improves over previous suggestions in
the literature to measure the gravitational wave background anisotropy based on
the time modulation of data as LISA orbits around the Sun. Such techniques,
however, are restricted only to certain combinations of spherical harmonic
coefficients of the galaxy with no ability to separate them individually. With
LISA, $m=2,3$ and 4 coefficients of the hexadecapole ($l=4$) can be measured
with signal-to-noise ratios at the level of 10 and above in a certain
coordinate system. In addition to the hexadecapole coefficients, when combined
with the time modulation analysis, the correlation study can also be used, in
principle, to measure quadrupole coefficients of the binary distribution.
