Wideband Spectrum Sensing via Derived Correlation Matrix Completion Based on Generalized Coprime Sampling

Wideband spectrum sensing is a popular topic in signal processing, especially for many radar and communication applications. What we face is a high sampling rate and a large volume of samples, in which demand of reducing the sampling rate without sacrificing the sensing resolution and quality. The generalized coprime sampling can break the limitation of the Nyquist sampling theorem with both characteristics of sparse sensing and coprime numbers. To fully utilize all the information received of the derived correlation matrix constructed by the different time delays, the matrix completion method is exploited. The theory of matrix completion is an extension of compressive sensing, though, which is not restrained by the sparsity and the restricted isometry property. The interpolation-based method presented via the convex framework of the nuclear norm minimization has no extra fine-tuned parameters, which different from techniques like compressive covariance sampling, positive definite Toeplitz matrix completion, and so on. Moreover, compared to the selection-based method under a continuous set, the proposed method improves the spectral resolution and estimation accuracy to avoid the information losing. The Simulation results indicate the performance of the algorithm.