Joint Estimation Of Frequency And DOAs For Multiple Sources Based On A Relaxed Coprime Sparse Array

The joint frequency and directions of arrival(DOA)estimation of source is the research hotspot and difficulty in the field of array signal processing.The existing joint frequency and DOA estimation algorithms almost are based on a uniform linear array,the signal samples will be obtained according with Nyquist sampling theorem and through data processing and transformation,the parameters estimation will generate.However,as the application frequency is increasingly high,it becomes difficult to design joint estimators for the frequencies and directions of arrival(DOAs)under the spatial-temporal undersampling condition.Specifically,on one hand,the temporal Nyquist theorem requires that the sampling rate be at least twice the highest frequency,which is unfordable for the existing analog-to-digital converters(ADCs);on the other hand,the spatial Nyquist theorem also requires that each inter-element spacing must be less than or equal to half the wavelength,which inevitably results in severe mutual coupling among sensors.Therefore,the research on frequency and DOA estimation based on sparse array has important research value.Focusing on the above problems,this paper presents a joint estimation algorithm of frequency and DOA based on a novel sparse array.First of all,this paper introduces a new type of sparse array —— relaxed coprime sparse array,and introduces its construction principle and method in detail.The relaxed coprime sparse array has a unique layout,i.e,every element of array has two ADCs.This array has two characteristics: 1)It allows a much higher array sparsity compared to the existing difference based coarrays;2)It allows to discretize an impinging signal with 2 sampling rates far lower than the signal frequency.In addition,the closed-form expression of the coprime sparse array is given in this paper,which makes it easy to apply the optimization in practical engineering.Secondly,this paper introduces the idea of closed form robust Chinese remainder theorem and spectrum correction.In the case of joint under-sampling in space-time domain,it is difficult for the traditional algorithms to effectively utilize the samples' information to achieve the signal parameter estimation.A new signal processing scheme is proposed to solve above problem in this paper,which utilizes the corrected spectral information and the Chinese remainder theorem to reconstruct the parameters.Thirdly,aiming at the narrow band incoherent signal from far field,this paper presents a joint frequency and DOA estimator for a single source based on the realxed coprime sparse array.This paper introduces the signal model of the algorithm and presents the detailed principle.At each sensor,a frequency estimate for the source object can be calculated through implementing the closed-form robust CRT on two frequency remainders,which are generated by applying the spectrum correction to the discrete Fourier transform results of two receiver sequences.Then,averaging these estimates at all sensors yields the final frequency estimate.On the basis of frequency estimation,the final DOA estimate can be calculated through implementing the closed-form robust CRT on all phase-difference remainders,which are also derived from the spectrum correction.The experimental results show that the proposed algorithm has higher accuracy and better noise robustness.Finally,based on the relaxed coprime sparse array,by incorporating the techniques of closed-form robust CRT,spectrum correction and pattern clustering,we propose a lowcomplexity multi-source joint frequency and DOA estimator under both temporal-domain undersampling condition and spatial-domain undersampling.our proposed joint estimator works well in both temporal-domain undersampling condition and spatial-domain undersampling condition,it suits well with the increasing tendency of spectrum utilization in higher frequency bands.Hence,our proposed estimator has a good prospect in a wide application fields such as radar,sonar,communication etc.This paper also presents a noise robustness analysis on both frequency estimation and DOA estimation,which is well verified by numerical results.