Fast, Efficient, and Viable Compressed Sensing, Low-Rank, and Robust Principle Component Analysis Algorithms for Radar Signal Processing

Modern radar signal processing techniques make strong use of compressed sensing, affine rank minimization, and robust principle component analysis. The corresponding reconstruction algorithms should fulfill the following desired properties: complex valued, viable in the sense of not requiring parameters that are unknown in practice, fast convergence, low computational complexity, and high reconstruction performance. Although a plethora of reconstruction algorithms are available in the literature, these generally do not meet all of the aforementioned desired properties together. In this paper, a set of algorithms fulfilling these conditions is presented. The desired requirements are met by a combination of turbo-message-passing algorithms and smoothed (Formula presented.) -refinements. Their performance is evaluated by use of extensive numerical simulations and compared with popular conventional algorithms.