Estimating and Tracking Wireless Channels Under Carrier and Sampling Frequency Offsets

This article addresses the challenge of estimating and tracking wireless channels under carrier and sampling frequency offsets, which also incorporate phase noise and sampling time jitter. We propose a novel adaptive filter that explicitly estimates the channel impulse response, carrier frequency offset, and sampling frequency offset by minimizing the mean-square error (MSE) and, when the estimated parameters are time-varying, inherently performs tracking. The proposed filter does not have any requirements for the structure of the waveform, but the digital transmitted waveform must be known to the receiver in advance. To aid practical implementation, we derive upper bounds for the filter's step sizes. We also derive expressions for the filter's steady-state MSE performance, by extending the well-known energy conservation relation method to account for the self-induced nonstationarity and coupling of update equations that are inherent in the proposed filter. Theoretical findings are verified by comparison to simulated results. Proof-of-concept measurement results are also provided, which demonstrate that the proposed filter is able to estimate and track a practical wireless channel under carrier and sampling frequency offsets.