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A robust adaptive beamforming technique based on a reconstructed covariance matrix and array steering vector (ASV) estimation using low-complexity algorithms is proposed. The spatial spectrum estimator is used to reconstruct the interference-plus-noise covariance matrix and the ASV estimation process is used to calculate the correlation coefficients of the assumed ASV and the eigenvectors. Contrary to other robust adaptive beamforming methods, this approach has better performance yet does not involve any specific optimisation programme even if arbitrary ASV imperfections are considered. Simple implementation and significant signal-to-interference-plus-noise ratio enhancement support the practicability of the proposed method.

Many modulated signals exhibit a cyclostationarity property, which can be exploited in direction-of-arrival (DOA) estimation to effectively eliminate interference and noise. In this paper, our aim is to integrate the cyclostationarity with the spatial domain and enable the algorithm to estimate more sources than sensors. However, DOA estimation with a sparse array is performed in the coarray domain and the holes within the coarray limit the usage of the complete coarray information. In order to use the complete coarray information to increase the degrees-of-freedom (DOFs), sparsity-aware-based methods and the difference coarray interpolation methods have been proposed. In this paper, the coarray interpolation technique is further explored with cyclostationary signals. Besides the difference coarray model and its corresponding Toeplitz completion formulation, we build up a sum coarray model and formulate a Hankel completion problem. In order to further improve the performance of the structured matrix completion, we define the spatial spectrum sampling operations and the derivative (conjugate) correlation subspaces, which can be exploited to construct orthogonal constraints for the autocorrelation vectors in the coarray interpolation problem. Prior knowledge of the source interval can also be incorporated into the problem. Simulation results demonstrate that the additional constraints contribute to a remarkable performance improvement.

With the augmentation of the non-zero conjugate correlation statistics of some modulating signals, enlarged degrees of freedom (DOFs) can be achieved with conventional sparse arrays as proposed by many literatures. But little research has been carried out on sparse array design with the augmented statistics. In this paper, a novel sparse array geometry which exploits both the correlation and conjugate correlation statistics is proposed. It stems from the prototype nested array with transposed subarrays. The sensor locations are determined systematically, and the closed-form expression for the achieved aperture under given number of physical sensors is derived. In our scheme, a new hole-free virtual array called the sum difference coarray is constituted with the proposed sparse array, in which all the lags are consecutive. Due to the output of the coarray is obtained by averaging the repeated lags generated by the addition and subtraction of the physical sensor location, the hole-free structure of the coarray enables all the lags engaged in averaging and makes the output of the coarray more stable. Moreover, the coarray has larger aperture than existing sparse arrays, so that bringing more degrees of freedom. In the end, simulations are conducted to demonstrate the superior performance of the proposed scheme over other existing structures.

A robust beamforming with quadratic constraints, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With this formulation, the constraints on magnitude response can be easily imposed on the adaptive beamformer. And the non-convex quadratic constraints can be transformed into linear constraints. Therefore, the proposed method can be robust against the steering direction error. In practice, there are many array imperfections except steering direction error. In order to resist all kinds of array imperfections, the adaptive beamformer based on worst-case optimization technique is proposed by minimizing the array output power with respect to the worst-case array imperfections. Simulation results demonstrate that the proposed method is effective and can achieve a better performance.

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