  The astrophysical Stochastic Gravitational Wave Background (SGWB) originates
from the mergers of compact binary objects that are otherwise undetected as
individual events, along with other sources such as supernovae, magnetars, etc.
The individual GW signal is time-varying over a time scale that depends on the
chirp mass of the coalescing binaries. Another timescale that plays a role is
the timescale at which the sources repeat, which depends on the merger rate.
The combined effect of these two leads to a breakdown of the time-translation
symmetry of the observed SGWB and a correlation between different frequency
modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB
due to binary black hole coalescence, calculated using simulations of different
black hole mass distributions and merger rates, we show how the structure of
the signal covariance matrix varies. This structure in the signal covariance
matrix brings additional information about the sources on top of the power
spectrum. We show that there is a significant improvement in the Figure of
Merit by using this additional information in comparison to only power spectrum
estimation for the LIGO-Virgo-KAGRA (LVK) network of detectors with the design
sensitivity noise with two years of observation. The inclusion of the
off-diagonal correlation in the covariance of the SGWB in the data analysis
pipelines will be beneficial in the quest for the SGWB signal in LVK frequency
bands as well as in lower frequencies and in getting an insight into its
origin.
