The performance of widely linear beamforming (WLB) is superior to adaptive beamforming, but it is limited by the uniform linear array geometry and non-uniform noise. In this paper, to overcome these limitations together, we propose a framework for widely linear beamforming in coprime array with non-uniform noise (WLB-CANUN). We subtract the non-uniform noise component from the coprime array sample covariance matrix, and vectorize the resulted matrix to create the difference co-array (DCA). Since the DCA is not uniform, we interpolate it and recover its signal by formulating the atomic norm minimization problem with the Toeplitz and orthogonal subspace constraints.The pseudo sample covariance matrix of coprime array does not contain the non-uniform noise component, which can be directly vectorized to create the sum co-array (SCA). Due to the non-uniformity of SCA, we interpolate it and recover its signal by formulating another atomic norm minimization problem with the Hankel and orthogonal subspace constraints. The directions of non-circular signals can be estimated by the traditional subspace method, which are utilized to estimate their non-circular coefficients. A least square optimization problem using the sample and pseudo sample covariance matrices of coprime array is formulated and solved to estimate the powers of non-circular signals. The interference-plus-noise covariance matrix (INCM), pseudo INCM and augmented INCM of coprime array are reconstructed, so that the ultimate augmented weight vector can be calculated. Simulation results indicate that the proposed WLB-CANUN method overcomes the limitations of WLB in coprime array with non-uniform noise, and enhances the performance compared to the existing WLB methods.

Coprime arrays have shown potential advantages for direction-of-arrival (DOA) estimation by increasing the number of degrees-of-freedom in the difference coarray domain with fewer physical sensors. In this paper, a new DOA estimation algorithm for coprime array based on the estimation of signal parameter via rotational invariance techniques (ESPRIT) is proposed. We firstly derive the observation vector of the virtual uniform linear array but the covariance matrix of this observation vector is rank-deficient. Different from the traditional Toeplitz matrix reconstruction method using the observation vector, we propose a modified Toeplitz matrix reconstruction method using any non-zero row of the covariance matrix in the virtual uniform linear array. It can be proved in theory that the reconstructed Toeplitz covariance matrix has full rank. Therefore, the improved ESPRIT method can be used for DOA estimation without peak searching. Finally, the closed-form solution for DOA estimation in coprime array is obtained. Compared to the traditional coprime multiple signal classification (MUSIC) methods, the proposed method circumvents the use of spatial smoothing technique, which usually results in performance degradation and heavy computational burden. The effectiveness of the proposed method is demonstrated by numerical examples.

This paper focuses on the distributed resource allocation problem of a second-order multi-agent system with external disturbances. The global network resource equality constraint is considered. A distributed algorithm with an exponential convergence rate is proposed based on an internal model for a known bounded disturbance. By using the active disturbance approach to design a reduced-order extended state observer, the proposed algorithm is modified to reject an unknown external disturbance. Moreover, exponential convergence is achieved through the Lyapunov theory when the disturbance is constant. When the differential of the disturbance is bounded, by adjusting the control parameter of the observer, the proposed algorithm converges to an arbitrarily small neighbourhood of the optimal solution. Finally, our simulation results demonstrate the effectiveness of our proposed algorithm.

Coprime array exhibits many advantages over the uniform linear array (ULA) with the same number of physical sensors in resolution performance and interference suppression capability. In this study, the authors take the advantages of coprime array to improve the robustness of adaptive beamformer. In the coprime virtual ULA (CV‐ULA), they prove that a constructed Toeplitz matrix can be taken as the sample covariance matrix from the perspective of virtual signal characteristics. The CV‐ULA Capon spectrum estimator is modified to obtain the directions and powers of all impinging signals. Since the real directions of all impinging signals are located at different angular sectors, they form independent signal subspace for each impinging signal. They also assign independent steering vector mismatches for different impinging signals to obtain their real steering vectors. The steering vector mismatch of each impinging signal is independently obtained by solving its own convex optimisation problem. They reconstruct the interference‐plus‐noise covariance matrix (INCM) with precise steering vectors and powers of interference signals. The proposed weight vector is computed by combining the desired signal steering vector and the reconstructed INCM. Extensive simulations show that the proposed algorithm provides robustness against many types of model mismatches.

It is well known that adaptive beamforming methods are susceptible to performance losses in the presence of model mismatches, especially when the training sample is contaminated by the desired signal. Here, in order to thoroughly remove the desired signal from the sample covariance matrix, the authors propose an iterative adaptive approach based on angular sector reconstruction algorithm to reconstruct the interference‐plus‐noise covariance matrix (INCM). Traditional INCM reconstruction methods are based on the Capon spectrum estimator to obtain the spatial power spectrum. However, the Capon spectrum cannot provide accurate power estimates because it is known to be sensitive to the array calibration error. Inspired by the excellent behaviour of the IAA algorithm, the authors use the IAA spectrum to obtain accurate power estimates which can be used to reconstruct the interference covariance matrix and revise the desired signal steering vector. Simulation results show that the performance of the proposed robust adaptive beamformer outperforms previous works and the output signal‐to‐interference‐plus‐noise ratios are close to the optimal values.