One-dimensional particle-in-cell (PIC) simulations are used to analyze the energy spectra measured by the New Horizons' Solar Wind Around Pluto (SWAP) instrument in the upstream region of an interplanetary shock observed at a distance of ~34 a.u. from the Sun. The use of individual populations simulating the different solar wind ion (SWI) and pickup ion (PUI) populations allow us to clearly identify the contribution of each population to the global energy spectra. The important role of shock front obliquity is stressed in the formation of PUIs streaming back along the magnetic field into the upstream region far from the front. Energy spectra measured by the SWAP experiment are well recovered in the present simulations. A detailed analysis shows that: (1) the highest energy part of the spectrum is formed primarily by both backstreaming PUI-H + and PUI-He + ; (2) the mid-range part of the energy spectrum is composed of both solar wind SW-H + and SW-He 2+ incoming ions that are superimposed on the PUI-H + population, and (3) the low energy range is composed of incoming PUI-H +. The agreement between experimental and simulation results is improved by using an initially filled-shell distribution for the PUI-H + population (instead of a zero-thickness shell), since this affects the low energy part of the spectrum strongly. This means that PUI-H + ions have sufficient time to diffuse onto and fill out a shell distribution after their initial pick up in the heliosphere, indicating that the subsequent cooling has an important impact on the global energy spectrum.