Abstract
Recently developed super nested array families have drawn much attention owing to their merits on keeping the benefits of the standard nested arrays while further mitigating coupling in dense subarray portions. In this communication, a new mutual coupling model for nested arrays is constructed. Analyzing the structure of the newly formed mutual coupling matrix, a transformation of the distorted steering vector to separate angular information from the mutual coupling coefficients is revealed. By this property, direction of arrival (DOA) estimates can be determined via a grid search for the minimum of a determinant function of DOA, which is induced by the rank reduction property. We also extend the robust DOA estimation method to accommodate the unknown mutual coupling and gain-phase mismatches in the nested array. Compared with the schemes of super nested array families on reducing the mutual coupling effects, the solutions presented in this paper has two advantages: (a) It is applicable to the standard nested arrays without rearranging the configuration to increase the inter-element spacing, alleviating the cross talk in dense uniform linear arrays (ULAs) as well as gain-phase errors in sparse ULA parts; (b) Perturbations in nested arrays are estimated in colored noise, which is significant but rarely discussed before. Simulations results corroborate the superiority of the proposed methods using fourth-order cumulants.
Highlights
Sensor array signal processing is a significant research area owing to its wide applications to radar, sonar, navigation, wireless communications, et al [1,2,3,4]
We provide a proof that the distorted steering vector can be factorized into a new matrix, including angular information only, multiplied by the coupling coefficient vector. Leveraging this property, we develop a MUSIC-like estimator to determine the direction of arrival (DOA) estimates based on the rank reduction (RARE) technique in the context fourth-order cumulants (FOC)
Analytical specifications show that our solutions are more robust to array imperfections as compared to the standard nested array processing
Summary
Sensor array signal processing is a significant research area owing to its wide applications to radar, sonar, navigation, wireless communications, et al [1,2,3,4]. In [39], the super nested array in the context of the second-order statistics is designed to significantly mitigate the cross talk between sensors while preserving all advantages of the standard nested arrays, by increase the inter-element spacing of the inner ULA to maintain the coarray but alleviate the adverse electromagnetic effects. To obtain more robust estimates, we would deal with these two issues from another perspective—consider the array imperfections and jointly resolve DOAs and the parameterized perturbations—rather than reduce the errors by a new geometry design This idea is reasonable in the sense that the super nested arrays and its successors occupying large areas are not applicable to some circumstances, such as airborne platforms, with a limited space for devices.
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