Research On Sampling Of Pulse Sequence With Finite Rate Of Innovation Based On Spectrum Information

Pulse sequences are widely used in the fields of radar,communications and biomedication.At present,the sampling equipments of pulse sequences are mostly based on Nyquist sampling theorem,which requires that the sampling rate is greater than or equal to twice the signals' bandwidth.However,with the development of modern technology,the bandwidth of pulse sequences becomes wider,which brings great challenges to the design of the sampling system,as well as the storage,transmission and real-time processing of the sampling data.The recent developed Finite Rate of Innovation(FRI)sampling theory can be used to design a specific structure with the parametric characteristics of FRI signals,which achieves a low sampling rate related to the innovation rate as well as perfect signal reconstruction.The rate of innovation of a signal refers to the number of free parameters per unit time.Pulse sequences are typical FRI signals.Since the rate of innovation of pulse sequences is usually much lower than the signals' Nyquist frequency,FRI technology can greatly reduce the pressure of such signals on sampling,date storage,transmission and processing.According FRI sampling theory,pulse sequences can be perfectly reconstructed from a few number of moments or spectral information,i.e.,Fourier coefficients,of the signals.However,compared to the moments,acquiring the spectral information of pulse sequences is more stable and simpler to implement.In this paper,based on the spectral information of pulse sequences,researches are carried out on the FRI signal model,sampling structure and reconstruction method.The main research contents and contributions are as follows:1.For the purposes of enhancing the stability and noise resistance of the sampling system,a muti-channel FRI sampling method based on filter bank is proposed.However,to avoid spectrum aliasing,this method adopts a complex and redundant solution,which contains multiple modulating and filtering process.To solve this problem,a simplified multi-channel FRI sampling method based on staggered modulation is proposed in this paper.The core idea of this method is to obtain the real part of several discrete distributed sub-bands of Fourier coefficients of the input signal by staggered modulating,low-pass filtering and low-speed uniform sampling process,combing with the proposed spectrum de-aliasing algorithm.In the reconstruction,a sparsity based parameter estimation algorithm is proposed to recover the unknown parameters of the input pulse sequence,by using the obtained real part of Fourier coefficients.Since it is not necessary to avoid spectrum aliasing by multiple modulating and filtering process,the proposed method reduces the complexity of the sampling system,yet maintain a similar precision of parameter estimation with the muti-channel FRI sampling method based on filter bank2.In order to resolve the poor universality of the existing FRI methods for pulse sequence,that is,the sampling structures vary for different frequency spectrum of the pulses,a general FRI sampling method based on spread spectrum is proposed in this paper.The core idea of this method is to spread the frequency spectrum of any kind of pulses to baseband with the spread spectrum technology in Random Demodulation.In this way,a low-pass filter can be used to obtain a group of aliased Fourier coefficients,which contain all spectral information of the input pulse sequence.In the reconstruction,a sparsity based parameter estimation algorithm is proposed to recover the unknown parameters of the input pulse sequence,by using the obtained aliased Fourier coefficients.Since the sampling structure is irrelevant to the frequency spectrum of the input pulse sequence,the proposed method enhances the universality of the sampling system.3.FRI sampling theory has been recently extended to pulse sequence with unknown shapes,by modeling the unknown pulse with the sum of a number of known functions.In order to solve the problem of low reconstruction accuracy of the existing FRI sampling methods for pulse sequence with unknown shapes under noise and model mismatch situations,an optimization model based FRI sampling method is proposed.The core idea of this method is to obtain a few time domain and frequency domain samples of the input signal by using two sub-Nyquist sampling channels.These samples are used to build an objective optimization function with the purpose of minimizing the model matching error.After that,the optimization algorithms are introduced to find the optimal estimation of the unknown parameters.Although the proposed method has increased the number of samplers and the computational complexity of the reconstruction algorithm,it reduces the model matching error and improves the signal reconstruction accuracy under noise and model mismatch situations.