This paper presents the average performance of the adaptive minimum estimation-combining generalized selection combining (MEC-GSC) scheme when used in a cellular deployment. In evaluating the performance, we consider a practical cellular environment in which we adopt log-normal shadowing for the local mean on top of Rayleigh fading, under the assumption that a user equipped with MEC-GSC is located uniformly over a cell of circular shape. Our numerical and simulation results show that the scheme under consideration considerably reduces the average receiver complexity of channel estimation and the average power drain from the battery while satisfying the desired performance requirement