There is mounting evidence that plasma structure in nighttime equatorial F layer evolves from large-scale wave structure (LSWS) in the bottomside F layer. This process cannot be ignored because equatorial plasma bubbles (EPBs) arise from large-amplitude LSWS; and, because intense radiowave scintillations are associated with EPBs, understanding the LSWS-to-EPB process is a crucial step toward reliable Space Weather Forecasting. In this regard, the transequatorial propagation (TEP) experiment appears to be the most useful among available research instruments. After a lapse of 30 years, the TEP experiment has been resurrected; a goal of this research is to understand TEP measurements well enough so that they can be used to diagnose the LSWS-to-EPB process. Toward this end, new results are presented in two companion papers. Herein (P1), off-great-circle (OGC) propagation paths are shown to consist of two types, discrete and diffuse. The new findings include the following: (1) a generalized multireflection model that can explain most of the observed properties; (2) the discrete type is supported by multireflections from an unstructured upwelling, (3) the diffuse type is supported by reflections from plasma structure in EPBs; and (4) the observed east-west (EW) asymmetry can be explained in terms of a distorted upwelling or plasma structure along the west wall of an upwelling. In Paper 2 (P2), a second form of observed EW asymmetry is explained in terms of plasma structure, which is not aligned with the geomagnetic field. The findings strongly confirm a close relationship between upwellings, ESF patches, and OGC paths.