Adaptive Compressive Sensing For Wideband Streaming Signals

Recent years,compressive Sensing is one of the most popular topics in signal processing field,which is used to deal with signals that are sparse in a certain basis.Through exploiting the sparsity,compressive sensing can sample the sparse signal at sub-Nyquist rate without distortion through proper reconstruction.This technology drives the development of UWB wireless communication and signal processing.With the maturity of theoretical works on the compressive sampling,many researches are focused on the hardware implementation of CS theory for wideband analog signals and reconstruction algorithms for finite signals.When processing infinite streaming signals,the signal is divided into disjoint blocks and reconstructed respectively by CS algorithms,which will involve block artifacts and input-output delay.This paper focuses on the processing of infinite wideband streaming signals which have sparse representation in frequency domain.We compare the mainstream compressive sampling system AIC with MWC,and propose an adaptive reconstruction algorithms for streaming signals.The main contribution of this paper is described as follows:1)This paper introduces an alternative model for signals acquired by the AIC scheme with the aim of avoiding the main drawback of this compressive sampling-based scheme,i.e.,the fact that the input signals are commonly assumed to be periodic,that is,being themselves a sum of discrete tones,namely multitone.The AICsystem is then reformulated and converted to a standard CS format successfully.2)We investigate the problem of utilizing the Kalman Filter to reconstruct signals with sparse frequency content under a streaming CS framework.We develop a GaussianMarkov model of the sparse streaming signal under the Analog-to-Information Converter(AIC)hardware structure and propose an adaptive Kalman Filter for the reconstruction.Different from existing CS schemes for streaming signals,we exploit the correlations between the signals of two consecutive observation windows to model the process in the state transition form so that the Kalman Filter can be incorporated to obtain the convergent estimation of the input streaming signal.