  The consortium NANOGrav discovered the isotropic gravitational wave
background (GWB) with an amplitude of $h\sim 10^{-15}$ and a frequency of
$f\sim 10^{-8}$ Hz using observations of millisecond pulsars. We hypothesize
that the GWB is relic radiation left over from the merging stellar mass black
holes (SBHs) during Big Crunch at $z\sim 10^{10}$. The relic gravitational
waves are similar to the gravitational waves with $f\sim 10^2$ Hz discovered by
LIGO in 2015, taking into account a decrease in frequency by a factor $\sim
10^{10}$ due to the expansion of the Universe. We take as a basis the observed
spectrum of 139 SBHs, discovered by the LIGO observatory. Our model explains
well all the observed features of the GWB. Unlike all other GWB models, our
model predicts a sharp decrease in the GWB amplitude at frequencies
$f>3.5*10^{-8}$ Hz, reflecting the deficit of SBHs with masses $<4M_\odot$. The
SBMH mergers at Big Crunch should generate yet undiscovered GWB with a
frequency of $f\sim 10^{-(14-17)}$ Hz.
