Algorithm for time-delay interferometry numerical simulation and sensitivity investigation

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