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Practical issues in histogram and parameter estimation over fading channels with type-based multiple access (TBMA) sensor networks is addressed in this paper, where the parameter of interest is estimated through the histogram, or type, of the observations. Existing histogram estimators in the literature require the transmitted signal waveforms to be orthogonal to represent different observations. If the fading channels from the sensors to the fusion center are zero mean, channel state information (CSI) is required at the sensor side. However, in practice, the interference between the orthogonal waveforms, and channel estimation error (CEE) cannot be avoided. How these practical issues affect the histogram and parameter estimation is discussed in this paper. A unified framework for histogram and parameter estimation in the presence of interference and imperfect CSI is proposed. In the interference-free case, a novel histogram estimator is proposed, which does not require the knowledge of the channel statistics at the fusion center, and yields an asymptotically optimal estimator. This approach is then generalized to the presence of interference. The existing estimators without the knowledge of interference statistics are shown to be biased, which motivates the proposed asymptotically optimal estimators that utilize interference statistics. Moreover, the performance of the asymptotically optimal estimators are shown to deteriorate when the waveforms are not orthogonal. Simulation results corroborate our analysis.
Date of Publication: March 2008