Sparse Recovery and Non-stationary Blind Demodulation

Abstract

In this paper, we consider a general sparse recovery and blind demodulation model. Different from the ones in the literature, in our general model, each dictionary atom undergoes a distinct modulation process; we refer to this as non-stationary modulation. We also assume that the modulation matrices live in a known subspace. Through the lifting technique, the sparse recovery and blind demodulation problem can be reformulated as a column-wise sparse matrix recovery problem, and we are able to recover both the sparse source signal and a cluster of modulation matrices via atomic norm and the induced ` 2,1 norm minimizations. Moreover, we show that the sampling complexity for exact recovery is proportional to the number of degrees of freedom up to log factors in the noiseless case. We also bound the recovery error in terms of the norm of the noise when the observation is noisy. Numerical simulations are conducted to illustrate our results.