Compressed Sensing Maximum Likelihood Channel Estimation for Ultra-Wideband Impulse Radio

One of the most attractive features of ultra-wideband impulse radio is the collection of rich multipath with the transmission of ultra-short pulses. Exploiting the rich multipath diversity with channel estimating Rake receivers enables significant energy capture, higher performance and flexibility than suboptimal receivers. Although data-aided (DA) maximum likelihood (ML) channel estimator shows a promising performance, its implementation is restricted by the Nyquist sampling criterion. The emerging theory of compressed sensing (CS) describes a novel framework to jointly compress and detect a sparse signal with fewer samples than the traditional Nyquist criterion. In this paper, we propose a CS-ML channel estimator which combines the compression framework of CS for sampling rate reduction while retaining the noise statistics formulation of ML to achieve a reliable performance. Simulation assessment indicates that, with far fewer measurements, the performance of our proposed scheme supersedes that of the 4-norm minimization estimator of CS and can be as close as the ML, but with a reduction in complexity.