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Ultrawideband (UWB) communications involve very sparse channels, because the bandwidth increase results in a better time resolution. This property is used in this paper to propose an efficient algorithm that jointly estimates the channel and the transmitted symbols. More precisely, this paper introduces an expectation-maximization (EM) algorithm within a wavelet-domain Bayesian framework for semiblind channel estimation of multiband orthogonal frequency division multiplexing based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding ldquoinsignificantrdquo wavelet coefficients from the estimation process. Simulation results using UWB channels that were issued from both models and measurements show that, under sparseness conditions, the proposed algorithm outperforms pilot-based channel estimation in terms of the mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, whereas the computational complexity is reduced compared with traditional semiblind methods.