Abstract
A recursive Bayesian approach to narrowband beamforming for an uncertain steering vector of interest signal is presented. In this paper, the interference-plus-noise covariance matrix and signal power are assumed to be known. The steering vector is modeled as a complex Gaussian random vector that characterizes the level of steering vector uncertainty. Applying the Bayesian model, a recursive algorithm for minimum mean square error (MMSE) estimation is developed. It can be viewed as a mixture of conditional MMSE estimates weighted by the posterior probability density function of the random steering vector given the observed data. The proposed recursive Bayesian beamformer can make use of the information about the steering vector brought by all the observed data until the current short-term integration window and can estimate the mean and covariance of the steering vector recursively. Numerical simulations show that the proposed beamformer with the known signal power and interference-plus-noise covariance matrix outperforms the linearly constrained minimum variance, subspace projection, and other three Bayesian beamformers. After convergence, it has similar performance to the optimal Max-SINR beamformer with the true steering vector.
Highlights
Digital beamforming is widely used in array signal processing for enhancing a desired signal while suppressing interference and noise at the output of an array of sensors [1,2]
Compared to the recursive Bayesian beamformers of [25,26], our method shows some improvements in terms of output signal-to-interference-plus-noise ratio (SINR) and beampattern shape, especially in the case of high signal-to-noise ratio (SNR)
By assuming that the steering vector is a complex Gaussian random vector, the beamformer can be viewed as a mixture of conditional minimum mean square error (MMSE) estimates weighted by the posterior probability density function (PDF) of the random steering vector
Summary
Digital beamforming is widely used in array signal processing for enhancing a desired signal while suppressing interference and noise at the output of an array of sensors [1,2]. We develop a narrowband beamformer using the Bayesian approach based on [25,26,28] In this approach, the interference-plus-noise covariance matrix and signal power are assumed to be known, and the steering vector is assumed to be a complex Gaussian random vector that characterizes the level of steering vector uncertainty. Unlike DOA, random modeling for the steering vector can address the uncertainties due to pointing error and the uncertainties due to scattering around the source, miscalibration, array deformation, different gain, and phase responses of sensors in the array, etc These three methods all apply the maximum a posteriori estimation for the uncertain DOA or steering vector and have the assumption that the interferers are located far away from the main lobe of the expected beamformer.
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