Joint Estimation of Carrier Frequency Offset and Channel Impulse Response for Linear Periodic Channels

In many communications scenarios, the channel exhibits periodic characteristics, e.g., power line communications and interference-limited communications. Additionally, certain approximations for mobile radio channels over finite time intervals may result in periodic channel models. In this paper, we study pilot-aided joint estimation of the channel impulse response (CIR) and of the carrier frequency offset (CFO) for linear periodic channels, in which both the CIR and the noise statistics vary periodically in time. We first consider the joint maximum likelihood estimator (JMLE) for the CIR and the CFO, and discuss the practical drawbacks associated with this estimator. When the coefficients of the delay-Doppler spread function of the CIR are approximately sparse, we propose two estimation schemes with higher spectral efficiency and lower computational complexity compared with the JMLE, which are obtained by exploiting both the periodicity and the sparsity of the channel, without requiring a priori knowledge of the sparsity pattern. Finally, we study the design of pilot sequences aimed at improving the estimation performance in sparse periodic channels. Simulation studies corresponding to practical scenarios of the proposed estimators demonstrate that substantial benefits can be obtained by properly accounting for the sparsity and periodicity in the design of estimation schemes.