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Multipath arrivals in an ultra-wideband (UWB) channel have long time intervals between clusters and rays where the signal takes on zero or negligible values. It is precisely this signal sparsity of the impulse response of the UWB channel that is suitable for the application of compressed sensing (CS) theory. However, these multipath arrivals mainly depend on the channel models that generate different sparse levels (low-sparse or high-sparse) of channels according to which, the authors have analysed and chosen the best recovery algorithms which are suitable for the sparse level for each type of channel model. Criteria for evaluating the algorithms are based on computational complexity, ability to reduce the sampling rate and processing time. Besides, the results of this work are an open topic for further research aimed at creating an optimal algorithm specially for application of CS-based UWB systems.