Estimation Of Frequency And DOA With Spatio-temporal Sub-Nyquist Sampling Based On Chinese Remainder Theorem

Estimation of the frequency and Direction of arrival(DOA)of the incident signal has been a hot research topic in radar,sonar,wireless communication,etc.However,for those the incident frequencies higher than C-band,the traditional Nyquist sampling scheme in temperal domain and spatial domain will incur a lot of problems such as dataflow overload,cross-coupling between array sensors,accuracy degradation and even algorithm falfuction,etc.Thus,under-sampling scheme in temperal-spatial domain,in which ambiguity of frequency and phase can be removed,needs to be developed.This paper aims to achieve this goal by mean of Chinese Remainder Theorem &spectrum correction.Firstly,the basic CRT theory is summarized.In particular,considering that the traditional CRT suffers from the sensitivity of remainder errors(thus not suitable to heavy noisy circumstances)and heavy computation load(thus difficult to be realized in real time),the robust closed-form CRT is chosen to the estimation of array signal parameters.Secondly,for the temperal under-sampling case,this paper builds up its CRT model,in which the unambiguous frequency can be recovered from those remainders at multiple channels.Particularly,the Candan interpolater and the AM interpolater are respectively employed to correct the frequency remainders,thereby improving the accuracy of the frequency reconstruction.Furthermore,the theoretic analytic expression of the variance of the frequency estimate is also deduced.For the spatial under-sampling case,this paper also builds up its sparse array model,in which the interspacing should be appropriately specified in terms of CRT.Provided that the signal wavelength is known,the phase differences of adjacent array sensors can be used as remainders.In combination of the robust closed-form CRT,a highaccuracy DOA reconstruction can also be realized.Lastly,this paper also proposes a joint scheme of the frequency and the DOA integrating the aforementioned two undersampling estimators.This scheme takes both the single object and multiple object into considerations.By means of the spectrum correction,the frequency estimator and the DOA estimator can be effectively linked.Thereby,the joint estimator of single object is generated.Furthermore,due to the organic integration of spectrum correction and pattern clustering,the intractable problem of remainder grouping can be easily solved and thus the joint estimator of multiple objects can also be generated.Numerical results confirm the effectiveness of these two joint schemes.