The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the early 2030s, is a gravitational wave observatory in space designed to detect sources emitting in the millihertz band. In contrast to the present ground-based detectors, the LISA data are expected to be a signal dominated, with strong and weak gravitational wave signals overlapping in time and in frequency. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable foreground noise. In this work, we present a generic method for characterizing the foreground signals originating from a given astrophysical population of coalescing compact binaries. Assuming idealized detector conditions and a perfect data analysis technique capable of identifying and removing the bright sources, we apply an iterative procedure which allows us to predict the different levels of foreground noise.