Model-Aware Compressive Sensing with Applications to Channel Estimation in mmWave Systems

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The compressive sensing (CS) method represents are very powerful framework to solve nonlinear parameter estimation problems. By discretizing the parameter space, it is possible to write the original estimation problem as a high-dimensional, linear problem with sparsity constraints.  In this research proposal, our first goal is to develop and analyze the optimal integration of available continuous estimators, e.g., maximum likelihood methods, into CS based algorithms. Specifically, the CS based estimator for the discretized parameter is made aware of the continuous model, which is used by the continuous part of the estimator. We call this method Model-Aware CS (MA-CS). Our second goal is to apply MA-CS to channel estimation in millimeter wave (mmWave) communication systems, an emerging technology for 5G wireless infrastructure systems. The channel estimation becomes an extraordinary challenging task due to the particularities of the mmWave channel. Within MA-CS, it is possible to formulate a joint estimator that is comprised of a CS part for the delay parameter and a continuous part for the angular parameters of the wireless channel.