Robust adaptive beamforming using a Bayesian steering vector error model

We propose a Bayesian approach to robust adaptive beamforming which entails considering the steering vector of interest as a random variable with some prior distribution. The latter can be tuned in a simple way to reflect how far is the actual steering vector from its presumed value. Two different priors are proposed, namely a Bingham prior distribution and a distribution that directly reveals and depends upon the angle between the true and presumed steering vector. Accordingly, a non-informative prior is assigned to the interference plus noise covariance matrix R, which can be viewed as a means to introduce diagonal loading in a Bayesian framework. The minimum mean square distance estimate of the steering vector as well as the minimum mean square error estimate of R are derived and implemented using a Gibbs sampling strategy. Numerical simulations show that the new beamformers possess a very good rate of convergence even in the presence of steering vector errors

Signal waveform estimation in the presence of uncertainties about the steering vector

We consider the problem of signal waveform estimation using an array of sensors where there exist uncertainties about the steering vector of interest. This problem occurs in many situations, including arrays undergoing deformations, uncalibrated arrays, scattering around the source, etc. In this paper, we assume that some statistical knowledge about the variations of the steering vector is available. Within this framework, two approaches are proposed, depending on whether the signal is assumed to be deterministic or random. In the former case, the maximum likelihood (ML) estimator is derived. It is shown that it amounts to a beamforming-like processing of the observations, and an iterative algorithm is presented to obtain the ML weight vector. For random signals, a Bayesian approach is advocated, and we successively derive an (approximate) minimum mean-square error estimator and maximum a posteriori estimators. Numerical examples are provided to illustrate the performances of the estimators

Symmetric complex-valued RBF receiver for multiple-antenna aided wireless systems

A nonlinear beamforming assisted detector is proposed for multiple-antenna-aided wireless systems employing complex-valued quadrature phase shift-keying modulation. By exploiting the inherent symmetry of the optimal Bayesian detection solution, a novel complex-valued symmetric radial basis function (SRBF)-network-based detector is developed, which is capable of approaching the optimal Bayesian performance using channel-impaired training data. In the uplink case, adaptive nonlinear beamforming can be efficiently implemented by estimating the system’s channel matrix based on the least squares channel estimate. Adaptive implementation of nonlinear beamforming in the downlink case by contrast is much more challenging, and we adopt a cluster-variationenhanced clustering algorithm to directly identify the SRBF center vectors required for realizing the optimal Bayesian detector. A simulation example is included to demonstrate the achievable performance improvement by the proposed adaptive nonlinear beamforming solution over the theoretical linear minimum bit error rate beamforming benchmark

A Robust Nonlinear Beamforming Assisted Receiver for BPSK Signalling

Nonlinear beamforming designed for wireless communications is investigated. We derive the optimal nonlinear beamforming assisted receiver designed for binary phase shift keying (BPSK) signalling. It is shown that this optimal Bayesian beamformer significantly outperforms the classic linear minimum mean square error (LMMSE) beamformer at the expense of an increased complexity. Hence the achievable user capacity of the wireless system invoking the proposed beamformer is substantially enhanced. In particular, when the angular separation between the desired and interfering signals is below a certain threshold, a linear beamformer will fail while a nonlinear beamformer can still perform adequately. Blockadaptive implementation of the optimal Bayesian beamformer can be realized using a Radial Basis Function network based on the Relevance Vector Machine (RVM) for classification, and a recursive sample-by-sample adaptation is proposed based on an enhanced ?-means clustering aided recursive least squares algorithm

Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

It is well known that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch. Such mismatches can occur as a result of direction-of-arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer that is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then, a diagonal loading method is used to force the magnitude responses at the arrival angles between these two steering vectors to exceed unity. Therefore, this method can always force the gains at a desired range of angles to exceed a constant level while suppressing the interferences and noise. A closed-form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard MVDR beamformer

Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random steering vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR