On Limitations and Improvement of Differential Beam Forming Via Quadratic Eigenvalue Optimization
Bibliographic record
Abstract
Differential microphone arrays (DMAs) have attracted considerable attention for their high spatial gains and frequency-invariant spatial responses. However, they often face significant white noise amplification at low frequencies. One approach to mitigating this challenge is by increasing the number of microphones while fixing the order of the DMA, leveraging additional degrees of freedom to optimize the white noise gain (WNG). But this compensation of WNG can lead to beampattern distortion at mid and high frequencies. To address this issue, we recently explored an approach to designing differential beamformers with predefined WNG levels. This involves formulating beamforming as a quadratic eigenvalue problem (QEP) to efficiently derive optimal solutions without iterative processes, leading to the QEP-based differential beamformers. While it is successful in controlling WNG, this method is found to exhibit great and atypical performance degradation at lower frequencies in certain scenarios. In this paper, we illustrate this phenomenon using a two-stage structured beamformer as a case study and offer insights into why this occurs, along with proposing a solution.
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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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".