  We employ the method used by the GW-Universe Toolbox to generate a synthetic
catalogue of detection of stellar mass binary black hole (BBH) mergers. We
study advanced LIGO (aLIGO) and Einstein Telescope (ET) as two representatives
for the 2nd and 3rd generation GW observatories, and study how GW observations
of BBHs can be used to constrain the merger rate as function of redshift and
masses. We also simulate the observations from a detector that is half as
sensitive as the ET at design which represents an early phase of ET. Two
methods are used to obtain the constraints on the source population properties
from the catalogues: 1. parametric differential merger rate model and applies a
Bayesian inference on the parameters; and 2. non-parametric and uses weighted
Kernel density estimators. The results show the overwhelming advantages of the
3rd generation detector over the 2nd generation for the study of BBH population
properties, especially at a redshifts higher than ~2, where the merger rate is
believed to peak. With the simulated aLIGO catalogue, the parametric Bayesian
method can still give some constraints on the merger rate density and mass
function beyond its detecting horizon, while the non-parametric method lose the
constraining ability completely there. We also find that, despite the numbers
of detection of the half-ET can be easily compatible with full ET after a
longer observation duration, the catalogue from the full ET can still give much
better constraints on the population properties, due to its smaller
uncertainties on the physical parameters of the GW events.
