Study On Broadband Signal Receiving With Expansion Theory And Methods Using Nyquist Folding Structure

With the advancement of electronic technology,the need for wideband spectrum sensing exists among all industries extensively,for instance,radio detection equipment,reconnaissance receiver equipment,etc.However,the current level of development of the analog to digital converter(ADC)does not match for the growth of the digital signal processors.Moreover,the data contain lots of redundant information,sampled form the high-speed ADC based on the Nyquist sampling theorem,which brings a great challenge for the storage,transmission,and processing of the signal.Therefore,it is necessary to study the broadband signal receiving and expanding using the existing ADC.The thesis studies the broadband signal receiving and expanding under sub-Nyquist sampling deeply by starting with the structure of the receiver,based on the structure of the coprime sampling,periodic nonuniformly sampling,and Nyquist folding receiver(NYFR).1.The model of the second-order derived signal under the coprime sampling is proposed,based on the multi-rate sampling(MRS)structure,which is the power spectrum sensing of the received signal with the independent variable of the time delay.Through the interpolation method of the convex optimization,the full information of the received signal is sufficiently utilized,which can further extend the resolution of the power spectrum estimation for the coprime sampled signal.The spectrum sensing method based on the sparse matrix completion of the coprime sampled signal,compared with the methods of solving frequency ambiguity based on the Chinese remainder theorem(CRT)and spectrum reconstruction based on the compressive sensing(CS)kernel of the partial inverse discrete Fourier transform(IDFT),can advance the resolution and accuracy of the spectrum estimation.2.The coprime sampling is a special kind of the periodic nonuniformly sampling,based on the multi-coset sampling(MCS)structure,and the spectrum reconstruction of the coprime sampled signal based on the time series decomposed model.The model of the second-order derived signal under the periodic nonuniformly sampling is proposed by comparing the coprime sampling structure.The spectrum sensing method based on the sparse matrix completion of the periodic nonuniformly sampled signal is implemented under the low signal to noise ratio(SNR)conditions,through the interpolation method of the convex optimization.It can break through the constraints on the accuracy of the spectrum reconstruction for the periodic nonuniformly sampled signal based on the time series decomposed and CS theory.3.NYFR is a special kind of twice sparse sampling structure,based on the sparse sampling structure of analog to information convert(AIC).Each part of the CS model of the NYFR structure all has a clear physical meaning,which is different than the other AIC structure and keeps the primary structure of the received signal.For the conventional sparse signal,the sensing matrix of the NYFR has the weak restricted isometry property(RIP)under the CS reconstruction algorithm.Using the block sparse signal model,the sensing matrix of the NYFR extends the block restricted isometry property(BRIP)under the block CS reconstruction algorithm.The new possibility is shown that NYFR can be served as the wideband spectrum sensing system.4.Based on the analysis,NYFR has the characteristic of periodic nonuniform sampling.Therefore,it can be regarded as the unified framework for the structure of coprime and periodic nonuniformly sampling.The physical realization feature of NYFR expresses as coprime sampling.And the mathematical transformation feature behaves as the periodic nonuniformly sampling and the CS transform.Then the derived abstract feature acts as autocorrelation matrix completion based on the second-order derived statistics.Whereas,compared with the general periodic nonuniformly sampling,the spectrum of the sub-sampled signal from NYFR not only has the characteristic of spectrum shifting,also with bandwidth extension.Therefore,the spectrum reconstruction method of the received signal from NYFR based on the time series decomposed and the system parameter setting of NYFR based on the zero-sum game is proposed,which extends the nonuniform sampling theory.The above methods are verified by the numerical simulation,which can achieve the broadband signal receiving and spectrum expanding under sub-Nyquist sampling,providing a reference for solving the problems of the broadband signal receiving and processing using the existing ADC.