The classical multiple signal classification (MUSIC) algorithms mainly have two limitations. One is an insufficient number of snapshots, which usually causes an ill-posed sample covariance matrix in many real applications. The other limitation is the intense space-colored and time-white noise, which also breaks the separability between signal and noise subspaces. In the case of the insufficient sample, there are few signal components in the non-zero delay sample covariance matrix (SCM), where the space-colored and time-white noise components are suppressed by the temporal method. A set of non-zero delay sample covariance matrices are constructed, and a nonlinear object function is formulated. Hence, the sufficient non-zero delay SCMs ensure that enough signal components are used for signal subspace estimation. Then, the constrained optimization problem is converted into an unconstrained one by exploiting the Lagrange multiplier method. The nonlinear equation is solved by Newton’s method iteratively. Moreover, a proper initial value of the new algorithm is given, which can improve the convergence of the iterative algorithm. In this paper, the noise subspace is removed by the pre-projection technique in every iteration step. Then, an improved signal subspace is obtained, and a more efficient MUSIC algorithm is proposed. Experimental results show that the proposed algorithm achieves significantly better performance than the existing methods.

A large-scale array (LSA) inevitably encounter scenarios with a small number of samples, and its beamformer suffers from high computational complexity. High computational complexity prevents the system from being used in practical online engineering applications. The complex vector of the beamformer weights can be expressed as the product of training snapshots and the signal steering vector, and a coefficient vector, since the optimal weight vector is a linear combination of basis vectors of the signal-plus-interference subspace. In this study, a new adaptive beamformer is developed on the basis of the minimum variance distortionless response (MVDR) criterion and kernel techniques. The new beamformer only needs to compute the inversion of a low-dimensional Gram matrix instead of the high-dimensional sample covariance matrix, which significantly reduces the calculation cost. Moreover, an efficient loading parameter calculation method (only related to the received matrix and not required user-defined parameters) is derived, which can adaptively suppress the mismatches of the ill-conditioned Gram matrix. Furthermore, a fast version of the new beamformer is formulated for the LSA under the scanning mode. Simulation results demonstrate that the new beamformer achieves better performance and a lower computation load than existing algorithms for a small number of samples. Especially, insufficient samples and high computational complexity problems are more frequently aroused in the space-time broadband array signal processing. Interestingly, the new techniques can be successfully extended to wideband array signal processing and yield satisfactory beam pattern shapes.

It is well-known that classical direction of arrival (DOA) estimation methods work well in the case of large samples. However, these methods may be theoretically invalid in the case of small samples, which frequently occur in large array systems. Such a large array has two effects: i) The number of samples is relatively quite small, and ii) the dimension of samples is very large. To handle the above problems, a more appropriate method for solving DOA estimators in the case of high-dimensional and small samples is proposed in this paper. First, considering the special structure of received samples, an alternative well-estimated second-order statistic, known as the Gram matrix, is originally constructed to better utilize the spatial and statistical information of signals and noise contained by small samples. Second, two novel methods for estimating the number of targets are derived by combining the Gram matrix and information-theoretic criteria. Third, a novel object function and the corresponding algorithm based on the Gram matrix are designed to estimate the signal subspace more efficiently, and then the DOAs of targets are obtained by multiple signal classification methods. In particular, the theoretical analysis indicates that the improved signal subspace estimation algorithm only needs to decompose the low-dimensional Gram matrix instead of the high-dimensional sample covariance matrix. Finally, simulation results are provided to demonstrate the high accuracy and lower computational complexity of the proposed methods in the case of high-dimensional and small samples.

The hyper basis functions (HBF)-based MoM has been proven to be an efficient numerical method to analyze broadband electromagnetic scattering problems. However, this method costs a lot of time to reconstruct the impedance matrix and reduced matrix at each frequency point. In order to solve the above problem, a novel method combining HBF-based MoM and compressive sensing (CS) has been proposed in this paper. The proposed method first applies the characteristic modes (CM) derived at the highest frequency point as the HBF for solving the scattering problems at lower frequency points, and performs sparse transform of the induced currents as the sparse basis for the CS framework. Then the measurement matrix is constructed using the method of uniformly extracting the impedance matrix by rows to obtain stable calculation results. Finally, according to the prior condition that a few CM are sufficient to characterize the surface currents approximately, the recovery algorithm is simplified least square method to reconstruct the current coefficients. Numerical simulation results show that it can significantly improve the efficiency of solving broadband electromagnetic problems compared with HBF-based MoM.

This letter provides a solution to a robust adaptive beamformer used in remote sensing systems under the effect of two factors: i) the impulsive noise satisfying Gaussian mixture distribution and ii) unknown model mismatches, such as look direction errors, sensor location perturbations, etc. First, a beamformer output-based cost function is designed to effectively suppress the influence of impulsive noise. Second, the weight vector of the beamformer is regularized through norm constraints to reduce the impact of model mismatches. Furthermore, an efficient iterative scheme is established to quickly minimize the designed cost function based on their properties, and a robust adaptive beamformer can be obtained. Finally, computer simulations are presented to demonstrate the robust performance and fast convergence of the novel algorithm in the presence of impulsive noise and model mismatches.