Rao-Blackwellized Gauss–Hermite filter for joint state estimation in cyclic prefixed single-carrier systems

In this paper, a new joint carrier frequency offset (CFO) and channel estimator is proposed for wireless cyclic prefixed single-carrier (CP-SC) systems. A novel Rao-Blackwellized Gauss–Hermite filter (RB-GHF) and Bayesian filter for joint channel and frequency offset estimation is introduced. The resulting RB-GHF incorporates Kalman filters, each conditioned on a Gauss–Hermite integration (GHI) point. The RB-GHF requires less operational complexity than the original GHF. The RB-GHF is also shown to greatly outperform an extended Kalman filter (EKF)-based estimator, and performs at least as well as a Rao-Blackwellized particle filter (RB-PF) estimator.

► We approximate the posterior density of CFO via GHF.
► We combine a Rao-Blackwellization with GHF.
► We propose a systematic Bayesian filter without resampling.