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Emergence of gravitational wave (GW) astronomy revived the interest inexploring the low frequency GW spectrum inaccessible from the ground. SatelliteGW observatory DECIGO in its original configuration and the currently proposedsmaller scale B-DECIGO are aimed to cover deci-Hertz part of the GW spectrum,which fills the gap between LISA mili-Hertz and deca- to kilo-Hertz rangeprobed by ground-based detectors. In this paper we forecast the detection ratesof inspiraling double compact objects (DCOs) and the unresolved confusion noisefrom these sources in DECIGO and B-DECIGO. In the context of DECIGO we use, forthe first time, the population synthesis intrinsic inspiral rates of NS-NS,BH-NS and BH-BH systems. We also estimate the expected gravitational lensingrates of such sources for DECIGO and B-DECIGO. The result is that yearlydetection of DCOs inspirals for the DECIGO is of order of $10^4 - 10^5$, whilefor a much smaller scale B-DECIGO they are about $10^2 - 10^4$ depending on theDCO population considered. Taking into account that considerable part of theseevents would be detectable by ground-based GW observatories the added value ofDECIGO/B-DECIGO could be substantial. DECIGO will also be able to register$5-50$ lensed NS-NS inspirals and up to O(100) BH-BH inspirals. On thecontrary, predictions for the B-DECIGO are pessimistic: only the optimisticcommon envelope scenario of DCO formation could yield a few lensed BH-BHinspirals per year. We also address the question of the magnification bias inthe GW event catalogs of DECIGO and B-DECIGO.

Inspiraling double compact object detection and lensing rate -- forecast for DECIGO and B-DECIGO