Wideband Signal Parameter Estimation Based On Spatio-temporal Co-prime Sampling

Frequency and direction-of-arrival(DOA)are two important parameters of signal.Accu-rate estimation of these two parameters plays an important role in many areas,such as elec-tronic detection,source localization and so on.Co-prime sampling theories including temporal co-prime sampling and co-prime array appeared a few years ago which acts as a new kind of s-parse sampling theory.It can relive the burden of front-end hardware and reduce the subsequent computation complexity,so it is widely concerned at home and abroad.Temporal co-prime sam-pling theory mainly focuses on the case where the sampling spacings are MT and NT where M and N are co-prime integers,and T is the temporal Nyquist sampling interval.The autocorre-lation Rc(?)of the signal xc(t)can be estimated at all lags ?=kT using the sparse samples at t=kNT and t=kMT.In the process of spectrum estimation,the ambiguity resolution is not needed and the number of signals which can be detected in frequency domain is increased from O(M+N)to O(MN).The same conclusion can be obtained in the co-prime array theory by changing the temporal Nyquist sampling interval T into the spatial Nyquist sampling interval A/2.Starting from the double-rate co-prime sampling theory,we discuss and do some research on frequency spectrum estimation technique based on temporal co-prime sampling,DOA esti-mation technique based on co-prime array and joint frequency and DOA estimation technique based on spatio-temporal sampling which lay a good foundation for practice.Our achievements are as follows:1.Multi-rate co-prime sampling and super-resolution spectrum estimation method.To reduce the system sampling rate further and solve the model mismatch problem thoroughly,we extend double-rate co-prime sampling to multi-rate co-prime sampling and propose a super-resolution spectrum estimation method based on multi-rate co-prime sampling and use an in-novative support set reduction rule which can further decrease the complexity of our algorithm.In addition,to relieve the hardware burden and improve the frequency estimation resolution in the method of double-rate co-prime filter bank,a frequency spectrum estimation method based on the theory of multi-rate co-prime filter bank is proposed.Theory derivation and simulation experiment show that when the number of filters is fixed,the frequency resolution in our method is much higher than that in the double-rate co-prime sampling method.In addition,2.Joint frequency and DOA estimation based on spatio-temporal co-prime sampling.Firstly,by combining co-prime array with co-prime sampling,we construct the received sig-nal data model based on spatio-temporal co-prime sampling.The virtual received data in the coarray domain is obtained by vectorizing the spatio-temporal covariance matrix.Due to the fact that signal is sparse in spatial-frequency domain,we present a two-dimensional sparse re-covery method to make the best use of the degrees-of-freedom(DOFs)in spatial-frequency domain.In addition,to minimize the system sampling rate,we propose a rule of choosing the sptaio-temporal co-prime parameters.Lastly,we derive the cramer-rao bound(CRB)of join-t frequency and DOA estimation under spatio-temporal co-prime sampling and write out the closed-form.The sufficient and necessary condition under which the CRB exists is given.In the derivation process,we have some conclusions about the asymptotic properties.When the number of targets is fewer than the number of spatio-temporal physical samples,the CRB tends to zero with the signal-to-noise(SNR)going to infinity.In contrast,the CRB tends to a non-zero constant with the SNR going to infinity when the number of targets is fewer than the number of spatio-temporal physical samples.3.Robust frequency and DOA estimation based on spatio-temporal co-prime sampling.As known to us all,the sparse recovery method is based on the discretized grid while the tar-gets cannot fall onto the predefined grids in practice.This will lead to the model mismatch and spectral leakage and degrade performance.To solve this,we first propose an amending algo-rithm based on two-dimensional Taylor series expansions.The frequency mismatch term and angle mismatch term are incorporated into the received data model.Based on the above modi-fied model,an improved greedy algorithm and convex optimization algorithm are presented to obtain the two-dimensional mismatches.The 2D off-grid sources can be corrected to accurate positions.This method can improve the accuracy of joint frequency and DOA estimation ef-fectively.In addition,we do some research on the joint frequency and DOA estimation using two-dimensional super-resolution theory which is based on a grid-free model.We derive the robust two-dimensional recovery guarantee and give out the optimization method.4.Parameter estimation of wideband multi-band signal.Firstly,to reduce the complexity in the DOA estimation of sparse multiband signal,we propose a DOA estimation method based on co-prime array under the circumstance of temporal sub-Nyquist sampling.The co-prime array is adopted in spatial domain and multi-coset sampling is used in temporal domain.The hardware burden and the data size can be reduced further.The algorithm complexity is analyzed and simulation results demonstrate this.Secondly,based on the modulated wideband converter(MWC)system which is used for sub-Nyquist sampling of sparse multi-band signal,we propose a spectrum sensing method using co-prime array based MWC.Compared to the conventional MWC system,the system sampling rate can be reduced further.In addition,each sensor in our method is usually corrupted by independent noise for an array system which can be used for noise averaging and improve the SNR.Lastly,to estimate the spectrum of frequency hopping signal,we propose a dynamic sensing method based on time-segment.