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Time Segmented Beamforming via Dynamic Programming: Theory and Implementation
Manan Mittal · 2026-05-26 · via math updates on arXiv.org

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Abstract:In dynamic acoustic environments with time-varying interferers, effective beamforming requires identifying stationary regions over time. The Capon beamformer, a whitened matched filter constrained to maintain unity gain in the desired direction, theoretically relies on the instantaneous ensemble covariance matrix. Practical implementations rely on the batch Capon (or Sample Matrix Inversion), which estimates the sample covariance matrix (SCM) by averaging over a block of snapshots. This practical approach implicitly assumes that the data within the batch window is stationary and can be coherently combined. In non-stationary settings, a batch approach that averages over fixed or excessively long windows fails, as moving interferers smear the SCM and degrade the beamformer's nulling capabilities. To address this, this paper introduces a temporally segmented distortionless response beamformer. Inspired by the segmented least squares method, which fits piecewise polynomials to data while penalizing excessive segmentation to prevent overfitting, the framework extends practical Capon beamforming by incorporating data-driven temporal segmentation. This formulation minimizes output power while dynamically adapting the SCM estimation windows to local stationarity, offering a principled approach to tracking time-varying interferers.
Comments: 16 pages, 17 figures, Beamforming New Approach Regret Bounds
Subjects: Signal Processing (eess.SP); Sound (cs.SD); Audio and Speech Processing (eess.AS); Systems and Control (eess.SY); Optimization and Control (math.OC)
Cite as: arXiv:2605.24825 [eess.SP]
  (or arXiv:2605.24825v1 [eess.SP] for this version)
  https://doi.org/10.48550/arXiv.2605.24825

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Manan Mittal [view email]
[v1] Sun, 24 May 2026 02:35:00 UTC (17,280 KB)