efficient algorithms for estimating lsfcs with no aid of ssfcs by taking advantage of the channel hardening effect and large spatial samples available to a massive mimo base station are proposed . the lsfc estimates are of low computational complexity and require relatively small training overhead . in the uplink direction , mobile stations transmit orthogonal uplink pilots for the serving bs to estimate lsfcs . in the downlink direction , the bs transmits either pilot signal or data signal intended to the mss that have already established time and frequency synchronization . the proposed uplink and downlink lsfc estimators are unbiased and asymptotically optimal as the number of bs antennas tends to infinity .