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Third-generation gravitational wave detectors, such as the Einstein Telescopeand Cosmic Explorer, will detect a bunch of gravitational-wave (GW) signalsoriginating from the coalescence of binary neutron star (BNS) and binary blackhole (BBH) systems out to the higher redshifts, $z\sim 5-10$. There is apotential concern that some of the GW signals detected at a high statisticalsignificance eventually overlap with each other, and the parameter estimationof such an overlapping system can differ from the one expected from a singleevent. Also, there are certainly overlapping systems in which one of theoverlapping events has a low signal-to-noise ratio $\lesssim 4$, and is thusunable to be clearly detected. Those system will potentially be misidentifiedwith a single GW event, and the estimated parameters of binary GWs can bebiased. We estimate the occurrence rate of those overlapping events. We findthat the numbers of overlapping events are $\sim 200$ per day for BNSs and afew per hour for BBHs. Then we study the statistical impacts of theseoverlapping GWs on a parameter estimation based on the Fisher matrix analysis.Our finding is that the overlapping signals produce neither large statisticalerrors nor serious systematic biases on the parameters of binary systems,unless the coalescence time and the redshifted chirp masses of the twooverlapping GWs are very close to each other, i.e.,$|\mathcal{M}_{z1}-\mathcal{M}_{z2}|\lesssim10^{-4} \,(10^{-1})\,M_\odot$ and$|t_{\rm c1}-t_{\rm c2}|\lesssim10^{-2}\,(10^{-1})$\,s for BNSs (BBHs). Theoccurrence rate of such a closely overlapping event is shown to be much smallerthan one per year with the third-generation detectors.

Impacts of overlapping gravitational-wave signals on the parameter estimation: Toward the search for cosmological backgrounds