Some practical issues in parameter estimation over fading channels with type-based multiple access (TBMA) sensor networks is studied in this paper, where the parameter of interest is estimated through the empirical distribution of the observations. In the literature, the asymptotically optimal estimator requires the transmitted signal waveforms to be orthogonal to represent different observations. Meanwhile, the channels between the sensors and the fusion center need to be non zero-mean. If the channel is zero-mean, channel state information (CSI) at sensor side is required. However, in practice, imperfect CSI, or interference between the orthogonal waveform dimensions, such as synchronization error, cannot be avoided, and may be unknown at the fusion center. How these practical issues affect the asymptotic optimality of the existing estimator and its performance are discussed in this paper. A unified framework for estimation with these practical constraints is proposed, which includes the imperfect CSI and synchronization error as special cases. The conditions under which the asymptotically optimal estimator requires the knowledge of the channel or interference statistics at the fusion center are derived. Furthermore, how the interference affects the performance of the asymptotically optimal estimator is characterized. Simulation results corroborate our analysis.