Time Segmented Beamforming via Dynamic Programming: Theory and Implementation

2026-05-23

AI Summary

This work addresses the limitations of conventional batch Capon beamformers in dynamic acoustic environments, where the assumption of signal stationarity leads to distorted covariance matrix estimates and poor suppression of time-varying interferences. To overcome this, the authors propose a temporally segmented distortionless-response beamforming method that integrates dynamic programming and data-driven temporal segmentation into the Capon framework. Inspired by piecewise least squares, the approach adaptively partitions the signal into locally stationary intervals and adjusts the covariance estimation window accordingly. By preserving a distortionless output response while dynamically aligning the estimation window with the underlying signal statistics, the method significantly enhances tracking and suppression of nonstationary interferences, mitigates covariance ambiguity caused by fixed-length windows, and thereby improves the robustness and practicality of the beamformer.

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.

Problem

• beamforming
• non-stationary interference
• sample covariance matrix
• temporal segmentation
• dynamic acoustic environments

Innovation

• time-segmented beamforming
• dynamic programming
• Capon beamformer
• sample covariance matrix
• non-stationary interference