High-Dimensional MVDR Beamforming: Optimized Solutions Based on Spiked Random Matrix Models

Minimum variance distortionless response (MVDR) beamforming (or Capon beamforming) is among the most popular adaptive array processing strategies due to its ability to provide noise resilience while nulling out interferers. A practical challenge with this beamformer is that it involves the inverse covariance matrix of the received signals, which must be estimated from data. Under modern high-dimensional applications, it is well known that classical estimators can be severely affected by sampling noise, which compromises beamformer performance. Here, we propose a new approach to MVDR beamforming, which is suited to high-dimensional settings. In particular, by drawing an analogy with the MVDR problem and the so-called "spiked models" in random matrix theory, we propose robust beamforming solutions that are shown to outperform classical approaches (e.g., matched filters and sample matrix inversion techniques), as well as more robust solutions, such as methods based on diagonal loading. The key to our method is the design of an optimized inverse covariance estimator, which applies eigenvalue clipping and shrinkage functions that are tailored to the MVDR application. Our proposed MVDR solution is simple, in closed form, and easy to implement.