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To address the problems of traditional two‐level nested arrays (TTNA) with low degrees of freedom and high mutual coupling, a generalised two‐level nested MIMO radar array with high degrees of freedom and low mutual coupling for the direction of arrival (DOA) estimation is proposed. First, two coprime expansion factors are introduced in the TTNA to mitigate mutual coupling among array elements and enhance its degrees of freedom. Secondly, the range of consecutive lags and the total number of virtual array elements are derived in closed form under the structures of 'sum–difference co‐array'. Finally, utilising the atomic norm minimisation theory, the authors address the issue of discrete holes caused by different coprime expansion factors through filling in virtual arrays at discontinuities. Furthermore, a convex optimisation model to recover equivalent received signals from these filled virtual arrays is established, which is combined with a multiple signal classification algorithm for DOA estimation. Simulation results validate the rationality of the array structure and demonstrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Sparse arrays are of deep concern due to their ability to identify more sources than the number of sensors, among which the hole-free difference co-array (DCA) with large degrees of freedom (DOFs) is a topic worth discussing. In this paper, we propose a novel hole-free nested array with three sub-uniform line arrays (NA-TS). The one-dimensional (1D) and two-dimensional (2D) representations demonstrate the detailed configuration of NA-TS, which indicates that both nested array (NA) and improved nested array (INA) are special cases of NA-TS. We subsequently derive the closed-form expressions for the optimal configuration and the available number of DOFs, concluding that the DOFs of NA-TS is a function of the number of sensors and the number of the third sub-ULA. The NA-TS possesses more DOFs than several previously proposed hole-free nested arrays. Finally, the superior direction of arrival (DOA) estimation performance based on the NA-TS is supported by numerical examples. [ABSTRACT FROM AUTHOR]

To address the weakness that the difference co-array (DCA) only enhances the degrees of freedom (DOFs) to a limited extent, a new configuration called the generalized nested array via difference–sum co-array (GNA-DSCA) is proposed for direction of arrival (DOA) estimation. We consider both the temporal and spatial information of the array output to construct the DSCA model, based on which the DCA and sum co-array (SCA) of the GNA are systematically analyzed. The closed-form expression of the DOFs for the GNA-DSCA is derived under the determined dilation factors. The optimal results show that the GNA-DSCA has a more flexible configuration and more DOFs than the GNA-DCA. Moreover, the larger dilation factors yield significantly wider virtual aperture, which indicates that it is more attractive than the reported DSCA-based sparse arrays. Finally, a hole-filling strategy based on atomic norm minimization (ANM) is utilized to overcome the degradation of the estimation performance due to the non-uniform virtual array, thus achieving accurate DOA estimation. The simulation results verify the superiority of the proposed configuration in terms of virtual array properties and estimation performance. [ABSTRACT FROM AUTHOR]

In this letter, an enhanced coprime array with compressed inter‐element spacing is designed for direction of arrival estimation. First, we analyse and conclude that the 0th sensor of coprime array with compressed inter‐element spacing is redundant for the consecutive lags, thus it is rearranged to the negative part to obtain enhanced coprime array with compressed inter‐element spacing. Then, on the basis of discussing the effect of the shift sensor on the difference co‐array, the number of unique lags and the range of consecutive lags are derived. Theoretical properties show that the closed‐form expressions of coprime array with compressed inter‐element spacing and enhanced coprime array with compressed inter‐element spacing are similar, while more difference lags can be generated from the latter. Moreover, larger inter‐element spacing can slightly alleviate the mutual coupling. Numerical examples verify the advantages of enhanced coprime array with compressed inter‐element spacing in direction of arrival estimation over coprime array with compressed inter‐element spacing configuration and other coprime arrays. [ABSTRACT FROM AUTHOR]