In this paper, we consider the decentralized estimation over non-orthogonal multiple-access fading channels (MACs) with zero-mean channel coefficients in wireless sensor networks (WSNs). Using the type-based multiple-access (TBMA) with bandwidth extension transmission scheme, we introduce a low-complexity two-stage estimator and analyze its performance. It shows that the performance can be improved by allocating bandwidth among types, but the optimal bandwidth allocation scheme requires a priori information of the parameter being observed. We then introduce a broadcasting feedback method for the sensors to obtain the required information. This feedback scheme is more efficient and feasible than the channel state information (CSI) feedback over orthogonal MACs. Besides the estimation accuracy, we also evaluate the bandwidth efficiency of the proposed methods by introducing a metric as the bandwidth normalized performance gain in simulations. It shows that the proposed feedback and bandwidth allocation schemes outperform the TBMA with CSI feedback in non-orthogonal MACs and the optimal transmission scheme in orthogonal MACs at typical operating signal-to-noise ratio levels of the WSNs.