Hopping Time Estimation of Frequency-Hopping Signals Based on HMM-Enhanced Bayesian Compressive Sensing With Missing Observations

Abstract

The hopping time reflects the time-varying characteristics of frequency-hopping (FH) signals, which are essential parameters for the spectrum estimation of FH signals. In this study, we address the problem of estimating the hopping time of multiple FH signals in the case of missing observations. We adopt a uniform linear array (ULA) to receive multiple FH signals and obtain the spatial phase difference via Bayesian compressive sensing (BCS), which is defined as the spatial frequency. We construct a hidden Markov model (HMM) with spatial frequencies. The trained HMM and received spatial frequency sequence are used to estimate the spatial frequency of the transmitter, and the mutation of the spatial frequency is used to detect the hopping time. Simulation and comparison experiments show that the proposed method is superior to the existing approaches. The hopping time can be estimated with satisfactory accuracy, even when the number of randomly missing observations is as high as 30%.