Impacts of Gravitational-Wave Background from Supermassive Black Hole Binaries on the Detection of Compact Binaries by LISA

In the frequency band of Laser Interferometer Space Antenna (LISA), extensive research has been conducted on the impact of foreground confusion noise generated by galactic binaries within the Milky Way galaxy. Additionally, the recent evidence for a stochastic signal, announced by the NANOGrav, EPTA, PPTA, CPTA and InPTA, indicates that the stochastic gravitational-wave background generated by supermassive black hole binaries (SMBHBs) can contribute a strong background noise within in LISA band. Given the presence of such strong noise, it is expected to have a considerable impacts on LISA's scientific missions. In this work, we investigate the impacts of the SGWB generated by SMBHBs on the detection of massive black hole binaries (MBHBs), verified galactic binaries (VGBs) and extreme mass ratio inspirals (EMRIs) in the context of LISA, and find it crucial to resolve and eliminate the exceed noise from the SGWB to ensure the success of LISA's missions.