Research On Compressed Sensing Based Algorithms For Diagnosis Of Defective Array Elements

The technical advantages of array antennas,including strong directivity,high gain and electronically scanned beam have significantly improved the reliability,stability and real-time performance of detecting and tracking targets.They have been widely used in military and civilian fields,such as radar,mobile and satellite communications,and biomedical engineering.However,as the ever growing of the total number of array elements,coupled with the functionality deteriorated as a result of age,inevitably increases the probability of damaged array elements.Failed sensors impose negative impacts on the performance of radiation pattern,especially sensitive to Peak Side-lobe Level and Null Depth Level and Locations.When the number of broken elements accumulates to a certain degree,the characteristic of digital beamforming and the accuracy of direction-of-arrival estimation will be worsen,which weaken the detection and anti-jamming capability of the radar systems for weak targets.Therefore,it is of great importance in terms of theoretical and practical values on developing diagnosis algorithms for defective array elements.The most representative algorithms for array diagnosis are matrix method and back propagation algorithm.However,these algorithms require that the number of measurements should not be less than the number of array elements.When the number of array elements become large,both of them suffer from a significant amount of measurements.It should be pointed out that the data acquisition process in antenna measurements is a time consuming and laborious task,leading to extension of diagnosis time and reduction of diagnosis efficiency.Therefore,to investigate novel diagnosis algorithms,which can break the limit of required number of measurements while keeping the performance of diagnosis will play a direct influence on shorting time,improving efficiency and saving costs of array diagnosis.The introduction of Compressed Sensing in array diagnosis has provided a fresh solver with the purpose of reducing the number of measurements.There are three basic steps for applying Compressed Sensing to array diagnosis.In the case of the number of failed sensors far less than the total number of array elements,the sparse array is first constructed by subtracting the reference array without failures and the array with damaged sensors.Next,the observation matrix is designed according to the sampling strategies adopted in the measurements.Then the sparse recovery algorithms are developed to retrieve the excitation of the sparse array.After going through these steps,the goal of failure identification can be achieved.However,there are two basic flaws in these array diagnosis algorithms.In specific,the observation matrix constructed using structured random under-sampling strategy in far-field measurements satisfies Restricted Isometry Property in probability.In addition,the Restricted Isometry Property of observation matrix constructed via random under-sampling strategy in near-field measurements is unknown.Both of these shortcomings will play an adverse effect on accurate diagnosis with high probability.In this dissertation,the aim is to improve the probability of success rate of diagnosis in both far-field and near-field measurements,and the corresponding solutions are proposed with the following innovations:1.A Compressed Sensing based far-field diagnosis method for defective array elements using deterministic sampling strategy is investigated.The observation matrix deriving from structured random under-sampling strategy satisfies the Restricted Isometry Property in probability.There exists some particular cases in which this requirement cannot be achieved,result in a negative impact on the performance of accurate diagnosis with high probability.In order to overcome this limitation,a deterministic sampling strategy is proposed to avoid the random distribution of sampling positions in the case of prime array,therefore improves the probability of success rate of diagnosis.2.A Compressed Sensing based far-field diagnosis method for defective array elements using hybrid iterative shrinkage thresholding algorithm is explored.In the case of sampling positions which are distributed uniformly in angular domain or non-uniformly but with more densely samples in the maximum direction in sine domain,no priori information are at hand on the Restricted Isometry Property of observation matrix using these sampling strategies.In this case,an accurate diagnosis with high probability can not be guaranteed using L₁ norm minimization.In order to overcome this deficiency,a hybrid algorithm is proposed to retrieve the excitation of sparse array and improves the probability of success rate of diagnosis.3.A non-convex Compressed Sensing based near-field diagnosis method for defective array elements using perturbation technique is proposed.In near-field measurements,the Restricted Isometry Property of observation matrix is still unknown using existing sampling strategies,which plays an adverse influence on accurate diagnosis with high probability when taken L₁ norm minimization into consideration.A perturbation technique is introduced to overcome the problem of local minima of retrieved solutions derives from the non-convexity of objective function,therefore improves the probability of success rate of diagnosis.4.A non-convex Compressed Sensing based near-field diagnosis method for defective array elements using iteratively reweighted least squares is demonstrated.In near-field measurements,the Restricted Isometry Property of observation matrix is still unknown using existing sampling strategies,which still plays an adverse influence on accurate diagnosis with high probability when taken L₁ norm minimization into account.This method improves the probability of success rate of diagnosis,while reducing the diagnosis time effectively,which is particularly suitable for fast diagnosis of defective array elements in the case of the number of measurements,the number of failures and the signal to noise ratio are available.