DOA Estimation Of Narrowband Frequency Modulated Signals With Missing Time Samples

High-resolution DOA estimation is an important technique for spatial spectrum estimation and is widely used in radar,sonar,communications and biomedical applications.With respect to the DOA estimation of non-stationary signals,the most widely used techniques are subspace based methods,e.g.,the MUSIC algorithm and its variants.However,these methods are available only when the number of the sensors is larger than sources,due to the requirement of noise subspace.Time-frequency analysis can improve the limits and STFDs have been proposed as a natural means for array processing when dealing with frequency modulated signals that are localizable in the time-frequency domain.This paper considers the problem of DOA estimation of such frequency modulated signals in a multi-sensor platform,and our particular focus is the situation where the observations at each sensor contain missing time samples.The time-frequency distribution is highly contaminated by artifacts due to the missing data contaminated by impulsive noise or a result of fading,obstruction,making the traditional STFD difficult to apply.So the paper reconstructs the STFDs matrix and gets the improved sparse time-frequency MUSIC algorithm which bases on the time frequency MUSIC algorithm,as follow we make two improvements specifically:(1)By exploiting the fact that time-frequency distributions are sparsely represented in the time-frequency domain and share a common non-zero support across multiple sensors,the paper proposes a multi-sensor data-dependent adaptive kernel to effectively suppress the noise-like artifacts caused by missing samples and reduce the effect of cross-terms within the time-frequency distribution,then achieve improved time-frequency distribution reconstruction.To achieve this purpose,the optimization or kernel parameters is performed at the averaged ambiguity function over all sensors,instead of the ambiguity function obtained in each individual sensor.Once the kernel is designed,the corresponding multi-sensor time-frequency signal representation can be obtained through the utilizing the one-dimensional Fourier transform relationship between the instantaneous auto-correlation function and the time-frequency distribution,rather than the two-dimensional Fourier transform relationship between the ambiguity function and time-frequency distribution.(2)The paper extends CS-based time-frequency approaches into a multi-sensor platform to perform the DOA estimation.The one-dimensional CS reconstruction not only reduces the computation complexity,but also improves the performance as a result of enabling the consideration of local sparsity over each time instant.By exploiting continuous structure of the time-frequency signature,a novel Bayesian CS algorithm is adopted to recover the time-frequency distribution and obtain the common nonzero support of the time-frequency signature.In this paper,considering that the averaged time-frequency distribution has the same time-frequency structure as all the time-frequency distributions but more robust,we use the OMP algorithm to reconstruct the sparse time-frequency signatures.The obtained TFD at each sensor permits the formation of a STFD matrix from sparse observations with suppressed artifacts.As such,the time-frequency MUSIC is extended to a sparsity-based version,referred to as the sparse time-frequency MUSIC,to perform DOA estimation of such signals.The sparse time-frequency MUSIC inherits the advantages of the time-frequency MUSIC,such as signal enhancement and source discrimination,and achieves robust DOA estimation through significant artifact suppression and reliable time-frequency signature reconstruction.The effectiveness of the proposed the sparse time-frequency MUSIC is verified through simulation results.