A Large Scale Antenna System (LSAS) entails a large number M (tens or hundreds) of base station antennas serving a small number of terminals. LSASs demonstrate large gains in spectral and energy efficiency compared with conventional MIMO technology. Recently we proposed pilot contamination precoding/postcoding (PCP), which is based on limited cooperation between base stations. As the number of antennas grows PCP allows one to cancel the pilot contamination interference and to obtain near interference and noise free LSAS. In this paper, we focus on the uplink PCP and show that even in the case of a finite number of base station antennas, PCP yields very significant performance gain. In particular, for M=100 it gives a 60 fold increase in the 5% outage data transmission rates.