Two Bayesian methods for multipath propagation parameters estimation

We propose a Bayesian approach for multipath channel time delay estimation when the signal is received by a square-law detector. Two different methods are presented. The first one is applied when the signal is supplied at the output of the detector. On certain approximations, the derivation of the MAP (maximum a posteriori) estimator leads to optimize a l₁-norm criterion. In the second method, the signal is observed after demodulation and matched-filtering. We introduce a Bernoulli-Gaussian model to account for the sparse properties of the channel impulse response and solve the deconvolution problem using Monte-Carlo simulations. Comparisons between both algorithms are presented on simulations. They show that the second method leads to more accurate estimators, while justifying the validity of the approximations used in the first one