ADAPTIVE BAYESIAN BEAMFORMING FOR STEERING VECTOR UNCERTAINTIES WITH ORDER RECURSIVE IMPLEMENTATION

An order recursive algorithm for minimum mean square error (MMSE) estimation of signals under a Bayesian model defined on the steering vector is introduced. The MMSE estimate can be viewed as a mixture of conditional MMSE estimates weighted by the posterior probability density function (PDF) of the random steering vector given the observed data. This paper derives an adaptive closed form Kalman-filter implementation that updates the weight vector by successive incorporations of data collected from additional array elements in the steering vector. The performance of the Bayesian beamformer is compared against several robust beamformers in terms of mean square error (MSE) and output signal-to-interference-plus-noise ratio (SINR). 1. BACKGROUND The received data vector of an N-element sensor array at sample time k has the form x(k) =a s ∗ (k)+i(k)+n(k), (1) where s(k) is the desired signal with known power σ 2 s, a ∈ C N is the steering vector, i(k) is the interence and n(k) is the noise. Let Ri+n � E[(i(k) +n(k))(i(k) +n(k)) H] be the interference-plus-noise covariance. Let (·) ∗ , (·) T and (·) H be the complex conjugate, transpose and Hermitian transpose, respectively. Assume that s(k), i(k) and n(k) are zero mean, temporally white, complex Gaussian processes that are mutually independent to each other. In practice, the true steering vector often deviates from its presumed value for various reasons such as improper array modeling, asynchronous sampling, pointing error, miscalibration, or source motion. It is often reasonable to model thes