Joint Synchronization and Channel Estimation for GFDM Systems

Generalized frequency-division multiplexing (GFDM) is a potential multicarrier scheme for the fifth-generation wireless communication and beyond owing to its advantages over orthogonal frequency-division multiplexing (OFDM). Despite its benefits, GFDM systems are exposed to intercarrier and inter-symbol interferences due to the use of non-orthogonal filters, which make synchronization and channel estimation (CE) in GFDM systems more challenging than those in OFDM systems. Existing work treats frequency synchronization, time synchronization, and CE separately, leading to an accumulation of errors in synchronization, estimation, or both. To address this issue, we propose a method for joint synchronization and CE for GFDM systems. The proposed method employs an optimization strategy that maintains innermost optimization as a least squares (LS) problem. The optimal solution to the LS problem can be expressed explicitly, allowing convenient use in the subsequent steps; specifically, the optimization is performed first in the time synchronization, followed by frequency synchronization, and finally in the CE. In addition, based on the proposed approach, we can derive the Cramer-Rao lower bound (CRLB) exactly, whereas in other schemes, only the approximated CRLB is derived. We compare the performance of the proposed method with that of existing methods using the probability of perfect time synchronization and root mean square error as performance measures. The results reveal that over a wide range of signal-to-noise ratio, the proposed method of joint synchronization and CE improves accuracy and outperforms state-of-the-art methods.