Study On Methods Of Sub-Nyquist Sampling For Signals From Union Of Subspaces

Sampling is a common method for analog signals to be transformed into digital,and is the cornerstone of modern information systems.According to the Shannon sampling theory,the sampling rate is at least twice the maximum frequency of the bandlimited signal.As the fast development of modern information technology,the band of signals has become wider.The bandwidth of many communication and information systems is going to be broadened up to 1 GHz.So,how to sample the wideband signals at a lower rate than Nyquist rate has attracted wide attention in the academic community.The Finite Rate of Innovation(FRI)sampling uses the rate of innovation instead of the band to sample the signal.The rate of innovation is the freedom of the signal per unit of time.In wideband communication systems,the rate of innovation is far lower than the band for many signals.Thus,the FRI sampling can sample the FRI signals with a rate far lower than the Nyquist rate.So far,all the methods of FRI sampling are based on the condition that the waveform of the input signals is a prior,but the signal waveform is easily distorted by noise during the transmission process in practice.Therefore,exploring the FRI sampling when not previously knowing the waveform of the input signal means a lot.The MF algorithm proposed by some researchers in recent years can reconstruct the original signal even if the waveform changed,which approximates the waveform with the exponentials.This paper models the FRI signal with the union of subspace,and analyzes the FRI sampling based on model fitting.Due to the high complexity of MF,the Least Mean Square(LMS)algorithm and the adaptive Multilayer Perceptron(MLP)are introduced in this paper,with the long-and-short-term memories of the MLP approximated to the coefficients of the annihilating filter.Experimental results show that the long-term memory network of the adaptive MLP can be capable to the Cadzow denoising after being trained offline,and its short-term memory network can adaptively update the coefficients of the annihilation filter online,with both the complexity and the load of computation reduced and the physical realizability improved.At the same time,the reconstruction error of locations reduces up to 1/6 and the running time reduces by 4/5 at least,compared with the algorithm of MF under the same conditions.So,the overall performance of the proposed algorithm has been improved.