Compressed Sensing for Ultrawideband Impulse Radio

In this paper, ultrawideband (UWB) channel estimation based on the novel theory of compressive sensing (CS) is developed. The proposed approach relies on the fact that transmitting an ultra-short UWB pulse through a multipath channel leads to a received UWB signal that can be approximated by a linear combination of a few atoms from a pre-defined dictionary, yielding thus a sparse representation of the received signal. The CS reconstruction capabilities are exploited to recover the composite pulse-multipath channel from a reduced set of random projections using the matching pursuit algorithm. This reconstructed signal is subsequently used as a referent template in a correlator based detector. Extensive simulations show that for different propagation scenarios and UWB communication environments, the CS detector outperforms traditional correlators using just 1/3 of the sampling rate leading thus to a reduced use of analog-to-digital resources in the channel estimation stage.