Compressive sensing (CS) methods are currently embraced 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. Many algorithms have been developed that can solve such sparsity-constrained linear systems even if they are severely underdetermined. A crucial difficulty measure associated with a given problem is the restricted isometry constant (RIC) of the measurement matrix, which relates the observations with the unknowns. The algorithm is successful if the constant is below a threshold, which depends on the algorithm. The RIC quantifies the maximal amount of distortion that a sparse vector undergoes in the measurement process, i.e., when multiplied with the measurement matrix.
In this presentation we focus on the exploitation of additional structure in the vector of the unknowns. In particular, the RIC of a matrix is determined by those sparse vectors that are maximally distorted. If these harmful vectors are removed from the class of allowed vectors, the RIC shrinks. Within the context of block CS and model-based CS, it has been shown that such a procedure is indeed possible if the additional structural information can be expressed in terms of the support of the unknown vector. For example, it is possible to enforce a minimum separation of adjacent nonzero entries of the unknown vector. We propose a framework, model-aware compressive sensing (MA-CS), with which certain manifold structural constraints can be incorporated into CS algorithms. Such constraints arise in multi-dimensional parameter estimation problems. Our main application example is channel estimation in wireless communications and radar. In this estimation problem, the goal is to estimate several delay and angle parameters. If both parameters are discretized, the RIC of the corresponding measurement matrix grows very quickly. Within the MA-CS framework, it is possible to discretize only the delay parameters and use conventional estimators for the angle parameters and still perform a joint estimation.
Wolfgang Utschick completed several accredited industrial training programs before he received the diploma (’93) and doctoral degrees (’98) in electrical engineering, both with honors, from Technische Universität München (TUM). Since 2002 Dr. Utschick has been appointed Professor at TUM where he is director of the Signal Processing Chair (Professur für Methoden der Signalverarbeitung). Dr. Utschick teaches courses on Signal Processing, Stochastic Processes, and Optimization Theory in the field of Wireless Communications, Signal Processing Applications and Power Transmission Systems. Since 2011 he is serving as a regular guest professor at Singapore’s new autonomous university, Singapore Institute of Technology (SIT). He holds several patents in the field of multi-antenna signal processing and has authored and co-authored a great many of technical articles in international journals and conference proceedings. He edited several books and is founder and editor of the Springer book series Foundations in Signal Processing, Communications and Networking. Dr. Utschick has been principal investigator in multiple research projects funded by the German Research Fund (DFG). He is currently the coordinator and spokesman of the German DFG focus program Communications over Interference limited Networks (COIN) which is devoted to topics as cooperative communications, crosslayer design, ad-hoc wireless networks, etc. He is a member of the VDE and senior member of the IEEE, where he currently serves as an elected member for the IEEE SPS Technical Committee on Signal Processing for Communications and Networking and as the Chair of the German Signal Processing Section. In 2016 Dr. Utschick has been appointed Vice Dean for the TUM Department for Electrical and Computer Engineering.