GW number count can be used as a novel tracer of the large scale structure
(LSS) in the luminosity distance space (LDS), just like galaxies in the
redshift space. It is possible to obtain the ${D}_{L}-{D}_{A}$ duality relation with
clustering effect. However, several LSS induced errors will contaminate the GW
luminosity distance measurement, such as the peculiar velocity dispersion error
of the host galaxy as well as the foreground lensing magnification. The
distance uncertainties induced from these effects will degrade the GW
clustering from a spectroscopic-like data down to a photometric-like data. In
this paper, we investigate how these LSS induced distance errors modify our
cosmological parameter precision inferred from the LDS clustering. We consider
two of the next generation GW observatories, namely the Big Bang Observatory
(BBO) and the Einstein Telescope (ET). We forecast the parameter estimation
errors on the angular diameter distance ${D}_{A}$ , luminosity distance space Hubble
parameter ${H}_{L}$ and structure growth rate ${f}_{L}{\sigma}_{8}$ with a Fisher matrix
method. Generally speaking, the GW source clustering data can be used for
cosmological studies below ${D}_{L}<5$ Gpc, while above this scale the lensing
errors will increase significantly. We find that for BBO, it is possible to
constrain the cosmological parameters with a relative error of ${10}^{-3}$ to
${10}^{-2}$ below ${D}_{L}<5$ Gpc. The velocity dispersion error is dominant in the
low luminosity distance range, while the lensing magnification error is the
bottleneck in the large luminosity distance range. To reduce the lensing error,
we assumed a $50\mathrm{\%}$ delensing efficiency. Even with this optimal assumption,
the fractional error increased to $O(1)$ at luminosity distance ${D}_{L}=25$ Gpc.
The results for ET are similar as those from BBO. Due to the GW source number
in ET is less than that from BBO, the corresponding results also get a bit
worse.