Efficient implementation of the IAA-based Magnitude Squared Coherence estimator

Recently, a novel Magnitude Squared Coherence (MSC) estimator was proposed using the Iterative Adaptive Approach (IAA) algorithm. In this paper, we present a computationally efficient implementation of this estimator, exploiting the inherently low displacement rank of the necessary products of Toeplitz-like matrices, thereby allowing for the development of appropriate Gohberg-Semencul (GS) representations of these matrices. Together with relevant data dependent trigonometric polynomials, the presented implementation offers a substantial computational reduction as compared to earlier implementations. Numerical simulations along with theoretical complexity estimations illustrate the performance of the proposed algorithm.