Based on multi-link synchronous propagation measurements, we study the downlink performance of Coordinated Multi-point (CoMP) systems. The propagation measurements took place in an outdoor micro-cellular environment with two base stations (BSs) located 60 m apart, each equipped with two cross-polarized co-located antennas. We focus on the challenging case of having closely-located users with 0.5 m inter- user distance. We consider four virtual users, each equipped with two antennas, moving along various routes. The patterns of the users' antennas, including the user's body influence, are measured in static scenarios with an upper body phantom and a handset mockup in the LTE 2.5-2.7 GHz band. The users' composite channel matrices are constructed based on: 1) the propagation channel represented by the multipath components extracted from the propagation measurements and 2) the user- influenced antenna pattern. We first analyze the effect of the BS antenna polarization on the collinearity among the users' channel matrices. Then, we evaluate the effect of the BS antenna polarization on improving the system performance, where the performance is evaluated based on two criterion: the number of users that the system is able to serve in the same time-frequency resource, and the achievable sum-rate. It is found that using cross- polarized BS antenna improves the fairness and the sum-rate of the system. It is also found that, in contrast to the case of conventional co-located MIMO, the improvement gained by CoMP systems (with per-BS power control) from using cross-polarized BS antennas is mainly attributed to improving the multiplexing gain of the system while the system's effective power gain has insignificant contribution.