We consider a multiuser (MU) multiple-input multiple-output (MIMO) time-division duplexing (TDD) system in which the base station (BS) is equipped with a large number of antennas for communicating with single-antenna mobile users. In such a system the BS has to estimate the channel state information (CSI) that includes large-scale fading coefficients (LSFCs) and small-scale fading coefficients (SSFCs) by uplink pilots. Although information about the former FCs are indispensable in a MU-MIMO or distributed MIMO system, they are usually ignored or assumed perfectly known when treating the MIMO CSI estimation problem. We take advantage of the large spatial samples of a massive MIMO BS to derive accurate LSFC estimates in the absence of SSFC information. With estimated LSFCs, SSFCs are then obtained using a rank-reduced (RR) channel model which in essence transforms the channel vector into a lower dimension representation. We analyze the mean squared error (MSE) performance of the proposed composite channel estimator and prove that the separable angle of arrival (AoA) information provided by the RR model is beneficial for enhancing the estimator's performance, especially when the angle spread of the uplink signal is not too large.