Finite Rate Of Innovation Based On Deep Neural Network

The current communication system is mainly based on the Shannon sampling theory.With the development of Internet of Things technology,the communication system has a lot of redundancy although such a sampling method can fully represent the signal’s waveform which brings severe challenges to the data processing,storage and transmission.In recent years,the method of sampling at a rate lower than Nyquist rate by using characteristics of signals has become a hot topic.The sub-Nyquist sampling makes it possible to sample broadband signal at low speed.The finite rate of innovation(FRI)was proposed in 2002 as a framework od sub-Nyquist sampling.The FRI sampling uses the innovation rate of signal to replace the bandwidth of signal as sampling rate to sample the signal which can be represented by a finite number of parameters in unit time.The rate of innovation is the number of unknown parameters of the signal in a finite time.The parameters of signal can be estimated by reconstructing algorithm.However,the input signal’s waveform structure of FRI sampling system must be known in advance.In the practical system,the signal waveform structure will be affected by the non-ideal effects such as multipath effect and pulse width broadening cause a distortion of the waveform.Therefore,The study of FRI sampling method in the condition of unknown waveform structure is of great significance to the application of FRI sampling in practical system.In recent years,researchers solve the problem of unknown waveform structure by approximating the signals with unknown waveform structure by linear combination of several known functions,so that the FRI sampling system can still be reconstructed effectively under the condition of unknown waveform structure.In this paper,we model the distortion FRI signal and model fitting(MF)method of FRI sampling method is analyzed.Based on the FRI sampling framework,a deep neural network was introduced to map the signals with unknown waveform structure to the known waveform structure through the long-and short-term memories(LSTM)model,and the parameters of the FRI signals with unknown waveform structure were estimated by using the characteristics of polynomial reproduced kernel.Experimental simulation results show that,compared with the existing FRI reconstruction methods,the proposed method can effectively extract the characteristic sequence of distorted signals,thus reducing the degradation of FRI reconstruction performance caused by signal waveform distortion.Experimental results on data sets of distorted FRI signals show that,compared with existing FRI reconstruction methods,the proposed method reduces the influence of multipath effect and can still achieve effective reconstruction in the presence of four paths.The method in this paper improves the stability of FRI system effectively.Since the number of LSTM network layers is more than 2,the system reconstruction performance will improve slowly.Therefore,the three-layer LSTM network is the best number of network layers for FRI reconstruction.