Linear precoder design for peak-to-average power ratio reduction of generalized frequency division multiplexing signal using gradient descent methods

This article addresses linear precoder design for the peak-to-average power ratio (PAPR) reduction of the generalized frequency division multiplexing (GFDM) scheme. This design relies on minimizing various statistical parameters of the instantaneous power of the GFDM signal-including variance, second and third moments-using gradient-based optimization methods. In this regard, a general framework of four different scenarios, which employs the steepest descent and conjugate-gradient methods and utilizes two different approaches of fixed and dynamic step-sizing, is proposed. In the case of fixed step-sizing, the results demonstrate that the algorithm diverges in some scenarios and provides low-speed convergence for the others due to its inability in meeting the terminating threshold regarding minimizing objective function to a desirable level. However, dynamic step-sizing using the Wolf line search rule circumvents these drawbacks, outperforms the existing research, and converges in all scenarios to a precoder providing advantages in terms of design speed and achievable PAPR, while keeping the symbol error rate and out-of-band emissions at the ranges of the un-precoded GFDM systems. Moreover, the results confirm the comprehensiveness of the proposed framework in adapting to various GFDM statistical parameters and gradient methods.