Clairvoyant performance bounds for adaptive beamforming in pulse-echo imaging

In adaptive beamforming, the array signal processing adjusts its sensor delays and weights based on the incoming data. In conventional beamforming, these parameters are instead given from a predefined model. Adaptive beamformers can improve measurement precision by dynamically rejecting spatial interference. While an established theory is available on the behavior of adaptive beamformers in textbook scenarios, their expected performance on realistic pulse-echo imaging scenes is still mostly uncharted. Imaging performance can be evaluated by individual pixel precision and aggregated metrics such as resolution and contrast. The achievable gain is strongly related to the sparsity of the scene and the availability of data to appropriately estimate the spatial covariance matrix. In pulse-echo measurements, the nonstationary interference poses a special problem for adaptive beamforming, which is a current research question of academic and industrial interest. The current work establishes a performance bound for adaptive beamforming in simulated realistic pulse-echo scenarios. This is derived and numerically implemented as the clairvoyant minimum variance distortionless response beamformer. The proposed framework allows for an a priori assessment of the applicability of adaptive beamforming, for a given scenario. The performance of the implemented algorithms can be directly compared with the theoretical limit in a simulated environment.