Global navigation satellite system (GNSS) augmentation based on low earth orbit (LEO) satellite constellation can significantly shorten the convergence time of precision point positioning due to the large geometric diversities added by rapid moving LEO satellites. In LEO satellite navigation augmentation systems that enable rapidly convergent precise point positioning (PPP), LEO satellite antenna phase center variation (PCV) corrections are usually indispensable for precise ranging signal transmissions over the period of LEO-augmented PPP convergence. However, the rapid geometric changes of LEO satellites lead to fast changes in satellite antenna PCVs. Their satellite PCV correction frequency needs to be increased compared to its counterpart in a GNSS satellite, which makes the corresponding satellite antenna PCV correction difficult to a receiver. In this paper, the overall satellite antenna PCV requirements for three-dimensional decimeter level positioning precisions in the LEO-augmented fast PPP application are analyzed, when no LEO satellite antenna PCV correction models are needed. With the proposed scheme, the LEO-augmented fast PPP user can avoid storing tens or hundreds of high dimensional satellite antenna PCV correction matrices in the LEO satellite navigation constellation. The experimental results show that the LEO satellite antenna PCV fluctuations should lie in the range [-12.6, 8.1] mm for the L1 band, and in the range [-19.5, 19.2] mm for the L2 band, in the LEO-augmented decimeter-level precision PPP application where the receiver does not need to correct the LEO satellite antenna PCV.