Research On The Improvement Of The Co-prime Spectrum Analysis Based On Under-sampling Rate

Co-prime spectral analysis is an emerging approach to discriminate densely distributed components.This scheme can achieve high-band spectral analysis in a rate regardless of the constraint of Shannon theorem,in that it only requires two undersampling rate and integrates poly-phase filtering,DFT and statistical cross-correlation.However,the application of co-prime spectral analyzer is limited,for there are 3 aspects of defects in its theoretical framework as follows: 1)An improper filter configuration is likely to incur spectral leakage;2)The statistical cross-correlation consumes a large number of snapshots(i.e.,large latency).Furthermore,it is only suitable to estimate those components of integer times of frequency resolution;3)The spectral leakage tends to cause cross-term interference and spurious peaks.In order to solve the above the problems,this paper puts forwards the following3 aspects of improvements.Firstly,for the purpose of suppressing spectral leakage,we incorporate a closed-form all-filter filter with the controllable cut-off frequency into the design of the prototype filter,which can analytically calculate the filter coefficients instead of complicated design procedure.Secondly,in consideration of the exponential signal stimulus,the analytical expression of signal at individual stages is deduced.Based on this,a Chinese remainder theorem associated relationship between two two DFT output channel is built up.Further,in combination of a spectrum corrector,we develop an accurate frequency estimator consuming only a few snapshots.Thirdly,to remove the spurious peaks interference,based on a deep analysis of the mechanism of spurious peaks,we propose a synthesized co-prime analyzer which combines the original co-prime estimator with a 0.5-shifted complementary counterpart.With the adoption of the aforementioned modifications,the following performance improvements are achieved.Firstly,the configurable all-phase filter can greatly suppress the spectral leakage and inter-interferences,thereby making the panorama spectrum much cleaner.Secondly,for the single-tone case,the proposed estimator can acquire accurate frequency estimate using only a few snapshots(specifically,a fractional frequency estimate only consumes a latency of 6?8 snapshots).Thirdly,for the multiple-tone case,by integrating the complementary analyzer and a decision maker,the proposed analyzer can remove redundant spurious peaks.Besides,the frequency resolution is also doubled.In general,both theoretical deduction and numerical prove that,compared to the original co-prime analyzer,the proposed modified co-prime analyzer achieves performance improvements in several aspects,which present the vast potential in wideband spectrum sensing,design of high-band frequency meter,and array signal processing etc.