Sparsity-Based Time Delay Estimation Through the Matched Filter Outputs

In this letter, we deal with the problem of high-resolution time delay estimation (TDE) in multipath environments exploiting the matched filter (MF) outputs data. To this end, we develop a systematic post-processing framework, consisting of two sparsity-based algorithms and a refining procedure aimed at reducing the computational load. The TDE problem is formulated as a sparse signal recovery problem and efficiently solved resorting to a majorization-minimization paradigm and a cyclic procedure. At the design stage, we assume a complex-valued Gaussian distribution model for the MF samples and incorporate a module-product prior that promotes the sparsity more significantly than the conventional complex Laplacian distribution. The preliminary performance assessment, conducted on simulated data, shows that, at least for the considered parameter values, the proposed delay estimators approach the Cramér-Rao bound for different signal-to-noise ratios and bandwidths.