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• convergence analyses. • consensus-alternating direction method of multipliers. • general quadratically constrained quadratic programs. • monotonically non-increasing of augmented Lagrangian function value. • boundedness of augmented Lagrangian function. We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is monotonically non-increasing as long as the augmented Lagrangian parameter is chosen to be sufficiently large. Simulation results show that the augmented Lagrangian function is bounded from below when the matrix in the quadratic term of the objective function is positive definite. In such a case, the consensus-ADMM is convergent. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of direction-of-arrival (DOA) estimation of rectilinear or strictly second-order noncircular signals with a partly calibrated uniform linear array (ULA). Consider that the uncalibrated portion of the array suffers from unknown gains and phases, an extended data model corresponding to a virtual (extended) array is presented by taking the noncircularity of the signals into account. On this basis and given the signal subspace matrix associated with the virtual array, a linear equation is derived to determine the unknown gains and phases. Then, the DOAs are found through the eigenvalue decomposition of a matrix related to the signal subspace matrix and array gains and phases. Since spatial spectrum search is not required, the proposed method is computationally efficient. Moreover, it is able to handle at most 2 M − 3 rectilinear signals with a partly calibrated ULA of M elements, even though only two neighboring elements of the array are calibrated. Numerical results also demonstrate that the proposed method has remarkable performance superiority brought by the rectilinearity. [ABSTRACT FROM AUTHOR]

• Off-grid DOA estimation. • Grid-based DOA estimation. • Second-order Taylor approximation. • Proportionality relationship. • Block restricted isometry property. The problem of off-grid direction-of-arrival (DOA) estimation is investigated. We develop a grid-based method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship, which is empirically demonstrated to be useful in the sense that it increases the probability of the mixing matrix satisfying the block restricted isometry property. Simulation examples demonstrate the effectiveness and superiority of the proposed method against several state-of-the-art grid-based approaches. [ABSTRACT FROM AUTHOR]