On Differential Beamforming With Nonuniform Linear Microphone Arrays
Bibliographic record
Abstract
While differential beamforming with uniform linear arrays (ULAs) has been widely studied, there is little work so far regarding the design of differential beamformers with nonuniform linear arrays (NULAs). This paper attempts to shed some light on the principles of differential beamforming with NULAs. We define spatial difference operators with NULAs, where any order of the spatial difference of the observation signals can be represented as the product of a nonuniform spatial difference operator matrix and the observation vector. Consequently, the design of differential beamformers is performed in two stages. In the first one, a nonuniform spatial difference operator matrix is applied to the array observations, thereby yielding differential signals. In the second stage, beamformers are designed and applied to the obtained differential signals to optimize the array performance. Based on the defined spatial difference operators, we derive from some performance metrics a family of differential beamformers with NULAs, which include the maximum directivity factor (DF), the maximum white noise gain (WNG), and the maximum front-to-back ratio (FBR) differential beamformers. To compromise between the DF and array robustness, we also derive the parameterized maximum DF and parameterized maximum FBR differential beamformers. The null-constraint maximum DF and WNG differential beamformers are also developed so that some nulls can be placed in specified directions for interference suppression. Simulation results validate the theoretical analysis and justify the properties of the proposed methods.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".