Robust Beamforming by Linear Programming
Bibliographic record
Abstract
In this paper, a robust linear programming beamformer (RLPB) is proposed for non-Gaussian signals in the presence of steering vector uncertainties. Unlike most of the existing beamforming techniques based on the minimum variance criterion, the proposed RLPB minimizes the ℓ∞-norm of the output to exploit the non-Gaussianity. We make use of a new definition of the ℓp-norm (1 ≤ p ≤ ∞) of a complex-valued vector, which is based on the lp-modulus of complex numbers. To achieve robustness against steering vector mismatch, the proposed method constrains the ℓ∞-modulus of the response of any steering vector within a specified uncertainty set to exceed unity. The uncertainty set is modeled as a rhombus, which differs from the spherical or ellipsoidal uncertainty region widely adopted in the literature. The resulting optimization problem is cast as a linear programming and hence can be solved efficiently. The proposed RLPB is computationally simpler than its robust counterparts requiring solution to a second-order cone programming. We also address the issue of appropriately choosing the uncertainty region size. Simulation results demonstrate the superiority of the proposed RLPB over several state-of-the-art robust beamformers and show that its performance can approach the optimal performance bounds.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".