Recently, the increasing demand for online services and applications has motivated a growing need for systems with higher data rates, improved link reliability and capability of serving more users than conventional systems. There are many scenarios for the fifth generation mobile communication systems in order to accomplish these objectives; such as: non-orthogonal multiple access, cooperative communications and network coding, self-organized networks, full-duplex device-to-device methods, mmWave communications, cognitive radio networks and, green communications. One of the serious candidates is Massive MIMO, as an emerging technology. In Massive MIMO, by increasing the number of antennas at the Base Station (BS) unboundedly, the simplest form of user detection, i.e. Matched Filter (MF), will be optimal. Also, it would be possible to highly reduce the effect of receiver noise and inter-user interference. Nevertheless, achieving these points depends on the availability of the perfect Channel State Information (CSI) that is impossible in practice. So, we have to rely on an estimate of the CSI by pilot-based or blind estimation methods. Because of the large number of users in Massive MIMO systems and their intra-cell and inter-cell mobility, the coherence time of the channels and consequently the number of available orthogonal pilot sequences will be limited. So, we have to reuse pilot sequences among all the cells. This results in “Pilot Contamination” that degrades the performance in the uplink detection and downlink precoding and cannot be circumvented by increasing the number of antennas. A number of methods have been proposed to reduce pilot contamination; e.g., EVD based channel estimation, pilot contamination precoding, filter bank multicarrier and improved MMSE estimation. Conventional MMSE has a great computational burden due to large size channel matrices in massive MIMO and the need for matrix operations such as matrix inversion. In the proposed method, we have shown that using a filter matched to the desired user’s pilot followed by estimation of the desired channels may reduce the complexity and computational burden. Keywords: Massive MIMO, Cellular systems, Pilot reuse, Pilot contamination, MMSE