FFT-Based Identification of Gilbert–Elliott Data Loss Models

Nowadays, radio- or Internet-based communication is gaining popularity in various fields, e.g., in signal processing. As these are not reliable real-time communications, some of the data are lost during the transmission. There are several stochastic models allowing the analysis of this phenomenon. The spectral properties of these models result in specific distortion in the signals' spectra. As the spectrum of the signal can easily be calculated via the fast Fourier transform (FFT), FFT-based identification methods of the data loss can be developed. In this article, a new identification method is proposed for the simpler cases of the Gilbert-Elliott model class. The article summarizes the mathematical description of data loss and introduces the Gilbert-Elliott model family. The novelty of the article is the identification method that is based on the autocorrelation function of the Gilbert-Elliott model. The proposed method is compared with classical procedures based on the Baum-Welch algorithm and the novel ones based on global optimization. The theoretical results are supported by extensive simulations.