Research On Space-time Adaptive Processing Methods For Airborne Radars With Coprime Arrays

With the development of radar technology and its application in the civilian field,an airborne radar with small weight,low cost,low power consumption and high clutter suppression performance has attracted much attention in recent years.Array positions in most of the existing airborne radars are arranged according to the Nyquist sampling theorem,which may result in same issues in airborne radar with high frequency band and high resolution,such as high hardware complex,serious array mutual coupling,high power consumption and high cost.Sparse array,such as minimum redundancy arrays,nested arrays,coprime arrays,can achieve increased virtual array sensors and array aperture,which can provide an effective method for the little weight,high frequency,low cost,low consumption and low coupling requirement.Compared to the minimum redundancy array,the nested and coprime arrays have rapidly received much attention due to their exact array position expression and easy realization.While coprime arrays have larger minimum inter-sensor spacing compared to the nested arrays and therefore mutual couplings between sensors for coprime arrays is smaller.Moreover,space-time adaptive processing(STAP)is a key technique for suppressing clutter and improving target detection in airborne radars.However,since the coprime array is a kind of sparse sampling,there are several difficulties for STAP with coprime arrays:(1)Conventional clutter rank estimation methods for uniform linear arrays cannot directly be applied as a result of the increased degrees of freedom of clutter or interference introduced by coprime sparse samplings.(2)Traditional methods of estimating covariance matrix via maximum likelihood estimation using the range training data cannot be applicable since the virtual signal model constructed from the covariance matrix of data received by coprime arrays is a rank one signal containing continuous and non-continuous sampling data.(3)The existence of array errors results in change of the equivalent virtual signal,and the robust STAP method under array errors becomes more complicated.Therefore,in this thesis,in order to solve these problems of clutter suppressing in airborne radars with coprime arrays,the STAP method for clutter suppression in airborne radars with coprime arrays is studies.The main contents and innovations are as follows:(1)The virtual equivalent signal model of airborne radar with coprime arrays and the clutter rank estimation method are studied.The virtual equivalent signal model for the cases of ideal array and the array error are established by exploiting the properties of increased degree of freedom and enlarged array aperture offered by coprime arrays.Based on the established signal model,for the case of the completely known the parameters and status of the airborne radar,the clutter rank estimation methods under the ideal case are given.For the case of the actual measurement errors,a robust clutter rank method based on bandwidth aperture product is proposed,where the two-dimensional space-time signal model is transformed into a one-dimensional equivalent space-domain signal model.Simulation results verify the effectiveness of the proposed methods.(2)The spatial-temporal smoothing based STAP methods for coprime arrays is studied.Aiming at the problem that the full-rank covariance matrix cannot be estimated by maximum likelihood method based on the rank one virtual snapshot,the spatial-temporal smoothing based STAP method for airborne radar with coprime arrays is proposed.The proposed method transforms the long single snapshot into multiple snapshots by using the spatial-temporal technique,which solves the issue that the clutter covariance matrix cannot be esimated based on the single snapshot.Simulation results reveal that the performance of the proposed method is much higher than that of STAP methods for data received by the physical array in the case of large number of samples.Moreover,the statistics distribution of the virtual snapshot and spatial-temporal smoothing matrix estimation errors is theoretically analyzed and shows that the estimation errors of the virtual snapshot and spatial-temporal matrix are inverse proportional to the number of training samples,exponential increased with increasing the clutter-to-noise ratio(CNR),and converge to a positive value.Moreover,we propose a reduced-dimension spatial-temporal smoothing based STAP method to improve the clutter suppression performance in low training sample support.(3)The sparsity-based STAP method for coprime arrays is studied.Considering the problems of insufficient utility of degrees of freedom and slow convergence of the spatial-temporal smoothing based STAP methods,a sparsity-based STAP method and a robust two-stage reduced-dimension sparsity-aware STAP method are proposed.The sparsity-based STAP formulates a sparse representation for the virtual equivalent signal model by exploiting the sparsity of the clutter,estimate the covariance matrix by using the high parameter resolution ability of sparse recovery methods,resulting in an improved clutter covariance matrix estimation accuracy.Simulations reveal that the sparsity-based STAP method can provide better performance and faster convergence than the spatial-temporal smoothing based STAP methods.The robust two-stage reduced-dimension sparsity-aware STAP method formulates a two-stage reduced dimension sparse representation model using the slow-time reduced-dimension and inaccurate knowledge,which reduces the dimension of the over-complete dictionary in the sparsity-based STAP method.Moreover,an OMP-like method is derived for estimating clutter subspace to tackle the problem of covariance matrix inversion in traditional STAP methods.Last,simulation results verify the effectiveness of the above mentioned methods.(4)The robust STAP method for airborne radars with coprime arrays in presence of array errors is studied.In practical radar system,the array errors may exist,resulting in model mismatch problem in sparsity-STAP methods for coprime arrays,and degrades the STAP method performance.Aiming at this issue,a robust sparsity-aware STAP method based on array error alternating iteration and a robust STAP method based on alternating direction method of multiplier(ADMM)method in presence of array errors are proposed.The former STAP method jointly estimates clutter spectrum and array errors via alternately iterating the focal underdetermined system solver(FOCUSS)and least squares(LS)methods,and then computes clutter covariance matrix based on clutter spectrum and array errors estimates.The latter method transforms the high computational complexity optimization problem of the clutter specturm and the array error into several sub-problems with low computational complexity,which reduces the low computational complexity.Simulations results show that the robustness of the proposed methods to moderate array errors.In summary,the STAP clutter suppression methods for airborne radars with coprime arrays studied in this paper can provide theoretical support for small airborne radar systems with low cost,low mutual coupling,and high frequency band.