Computationally Efficient Capon- and APES-Based Coherence Spectrum Estimation

Abstract

The coherence spectrum is of notable interest as a bivariate spectral measure in a variety of application, and the topic has lately attracted interest with the recent formulation of several high-resolution data adaptive estimators. In this work, we further this development with the presentation of computationally efficient implementations of the Capon- and APES-based MSC estimators. The presented implementations furthers the recent development of exploiting the estimators' inherently low displacement rank of the necessary products of Toeplitz-like matrices to include also the required cross-correlation covariance matrices for the mentioned coherence algorithms. Numerical simulations together with theoretical complexity measures illustrate the performance of the proposed implementations.