Enhancing the degrees of freedom (DOFs) of MIMO systems has been a hotspot in communications. In this letter, a novel strategy to construct difference coarray of the sum coarray (DCSC) with heightened DOFs for coprime MIMO systems is put forward. Using the polynomial of DCSC, we reveal that DOFs expansion for sparse MIMO systems is a replicate-and-shift (RS) procedure, which explains the deficiency of overlapping lags caused by the consecutive DOFs in the difference coarray (DCA) as a moving period. To tackle this problem, the moving period is raised to the number of DOFs, so that the lags and holes in the forward and backward periods can perfectly complement each other. The range of consecutive DOFs (cDOFs) and the number of DOFs are then described in the closed-form expressions. The results show that the proposed strategy generates more DOFs than previous studies.

In recent years, sparse arrays have made considerable strides in resolving uncorrelated sources. However, the ubiquitous coherent sources across various emerging applications pose unique challenges for direction-of-arrival (DOA) estimation with sparse arrays. In this work, based on insight into the structure of the source covariance matrix, we first propose an effective strategy to achieve decorrelation by partitioning the diagonal and off-diagonal elements in the source covariance matrix. Then, we introduce two Toeplitz matrix reconstruction programs tailored for DOA estimation with sparse arrays. On one hand, we directly implement the decorrelation operation on the covariance matrix of sparse arrays, and further construct a Toeplitz matrix reconstruction program via virtual array interpolation for enhanced DOA estimation. On the other hand, we relate the sparse array to the hypothetical uniform linear array (ULA) through the compressed matrix, and perform decorrelation operation on the covariance matrix of the hypothetical ULA. Following this, a Toeplitz matrix reconstruction program via physical array interpolation is formulated for DOA estimation. Unlike the prevailing decorrelation techniques, the proposed algorithms can precisely estimate coherent sources without losing degrees of freedom and array aperture. Moreover, the Cramér-Rao bound pertinent to this problem is derived. Numerical simulations demonstrate that the proposed algorithms outperform their competitors in estimating coherent sources.

Coprime array (CA) is a highly regarded sparse geometry for direction of arrival (DOA) estimation because it offers heightened degrees of freedom (DOF) and alleviated mutual coupling (MC) effect. Nevertheless, the appearance of holes in the difference co-array (DCA) of CA extremely shortens the continuous DOF (cDOF) available for spatial smoothing technique. To cope with this deficiency, we develop an augmented coprime array (ACA) in this paper by deploying a uniform subarray and one sensor at the left end and right end of CA, respectively. The placement of these additional sensors is determined by the analytical expressions and a two-dimensional (2D) representation that account for all the holes in the DCA of CA. The precise mathematical expressions for the attainable DOF and the first three weight functions of ACA are further derived, which show that ACA achieves the equivalent quantity of cDOF as the hole-free (super) nested arrays, while retaining a comparable level of MC effect to CA. Moreover, in comparison to the majority of advanced sparse array geometries, the devised ACA proves more effective at striking a balance between the quantity of cDOF and MC effect. Numerical examples are provided to confirm the outstanding characteristics of our designed ACA and its remarkable efficacy in DOA estimation.

A collocated multiple-input–multiple-output (MIMO) radar has the ability to track multiple targets in the simultaneous multibeam working mode, where the defocused beams are transmitted to illuminate the whole space, and focused beams are received to extract target information. A fast power allocation (FPA) strategy is put forward in this mode. The predicted posterior Cramer–Rao lower bound (PCRLB) in the cluttered background is slighted relaxed and utilized as the optimization metric. The optimization model is then established as minimizing the worst case of PCRLB under the constraint of total power budget. By using the monotonic decreasing and invertible properties of the relaxed PCRLB, a fast sequential relaxation-based solver is proposed for this problem solving. At each iteration, the proposed solver tests the power allocation (PA) to one target whether should be set as the minimum level. Simulation results show the effectiveness and efficiency of the proposed solver, compared with convex optimization-based methods. The results also imply that the target distance and reflectivity are two main factors that influence the PA in our strategy.