In this paper, end to end average bit error rate (BER) for three-hop cooperative communication systems with a decode-and-forward (DF) relay is derived in the closed-form in the presence of error propagation. The derived end-to-end BER expression is verified via computer simulations. It is shown that the threshold selection for the relays has dominant effect on the error performance of the system. In this paper, we multi-hop communication between base station and cell-edge users to achieve ultra-wide coverage which is one of the important requirements for 5G and beyond.