Algorithm for time-delay interferometry numerical simulation and sensitivity investigation

We introduce a generic algorithm to determine the time delays and spacecraft positions compose any time-delay interferometry (TDI) channel in dynamical case evaluate its sensitivity by using full numerical method. select 11 second-generation TDI channels constructed from four approaches investigate their gravitational wave responses, noise levels, averaged sensitivities under LISA orbit. The of selected are various especially for frequencies lower than 20 mHz. optimal ${\mathrm{A}}_{2}$ (or equivalently ${\mathrm{E}}_{2}$) combined Michelson (${\mathrm{X}}_{1}$, ${\mathrm{X}}_{2}$, ${\mathrm{X}}_{3}$) achieves best among channels, while Sagnac ${\ensuremath{\alpha}}_{1}$ shows worst sensitivity. Multiple show better at some characteristic compared fiducial ${\mathrm{X}}_{1}$ channel. joint ${\mathrm{A}}_{2}+{\mathrm{E}}_{2}+{\mathrm{T}}_{2}$ observation not only enhances factor $\sqrt{2}$ 2, but also improves capacity sky coverage.