Sparse Bayesian learning for interference-plus-noise covariance matrix reconstruction in robust MVDR beamforming

We propose an SBL-driven interference-plus-noise covariance matrix (INCM) reconstruction method for robust MVDR beamforming with limited snapshots and array-manifold uncertainties (primarily steering mismatch and interference-sector/DOA uncertainty). A multi-snapshot sparse Bayesian learning (SBL) model on a dense angular grid jointly infers a sparse angular power distribution and the noise variance from interference-contaminated data. The key contribution lies in a principled INCM synthesis mechanism outside a protected sector around a coarse look direction: (i) a noise-floor–calibrated screening rule with a threshold proportional to the SBL noise estimate (constant false-alarm rate (CFAR)-type behavior), (ii) an energy-coverage dominant-set selection that limits truncation error and mitigates leakage accumulation under small- L , and (iii) a direction–scale decoupled normalization that stabilizes interference-power scaling while preserving dominant directions. The resulting beamformer retains the closed-form MVDR structure by substituting the unknown steering vector and INCM with the proposed SBL-based estimates, without relying on any specific DOA retrieval algorithm. Under ideal on-grid and source-separation conditions, we characterize the population optimum of the SBL evidence objective in the covariance domain, providing an interpretation for asymptotic consistency and near-genie SINR behavior. Simulations demonstrate robust SINR gains over representative baselines across steering mismatch, contaminated training, and limited-snapshot regimes.