Several coherence function (CF) estimators have been proposed owing to their wide use in various kinds of field, such as signal detection, signal estimation and system identification. For short data records, the CF is often inaccurate because of a large variance. So, researchers all over the world tried to propose numerous approaches to reduce its variance.

Most of the existing methods are data-independent and often have to obtain smaller variance at the expense of introducing the wider main lobe. To solve this problem, researchers of Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences carried out a series of studies and introduced a new class of nonparametric coherence function (NPCF) estimators.

By introducing a nonlinear function of covariance matrix, the researchers present a generalized framework for NPCF estimation and also propose a novel low-variance and high-resolution CF estimator named after minimum variance multitaper CF (MVMT-CF). Moreover, this framework helps to understand the properties of several existing NPCF estimators more easily, including the single- and multi-window based approaches. Finally, tested by the practical experiments, the researchers conclude that by properly choosing the parameters of the generalized class of NPCF estimators, a good tradeoff between spectral resolution and variance can be achieved for different types of signals.