In this paper we study the depolarization effects caused by, rain and ice particles in the troposphere on the performance of a multiple HAP (High Altitude Platforms) system employing multi-polarized compact MIMO antenna configurations. In order to reinforce the analysis, we first propose a novel multi-channel simulator that produces realistic time-series of the fading process affecting signal transmission in HAP systems. The proposed simulator takes into account the temporal, spatial and polarization properties affecting these processes. Finally, we analyse the impact of depolarization on the total capacity of the system. Simulation results show a significant drop in performance as the cross polar discrimination decreases