  NANOGrav, EPTA, PPTA, and CPTA have announced the evidence for a stochastic
signal from their latest data sets. Supermassive black hole binaries (SMBHBs)
are supposed to be the most promising gravitational-wave (GW) sources of pulsar
timing arrays. Assuming an astro-informed formation model, we use the NANOGrav
15-year data set to constrain the gravitational wave background (GWB) from
SMBHBs. Our results prefer a large turn-over eccentricity of the SMBHB orbit
when GWs begin to dominate the SMBHBs evolution. Furthermore, the GWB spectrum
is extrapolated to the space-borne GW detector frequency band by including
inspiral-merge-cutoff phases of SMBHBs and should be detected by LISA, Taiji
and TianQin in the near future.
