We provide recovery guarantees for the model-aware OMP algorithm, which is an extension of the known block-OMP algorithm. The new algorithm exploits additional structural information about the unknown signal. This leads to successful recovery under weaker conditions on the sensing matrix, namely, a restricted isometry property with respect to structured signals, only. A possible application of this algorithm is for channel estimation in wireless communication systems where nonlinear delay and angle estimation problems need to be solved. For this application, our method only discretizes the delay parameter and not the angular parameter. As such, it is situated between very complex nonlinear maximum-likelihood estimation and very efficient compressive sensing based methods that discretize all parameters.
['Thomas Wiese', 'Lorenz Weiland', 'Wolfgang Utschick']
Exact recovery of structured block-sparse signals with model-aware orthogonal matching pursuit