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

Abstract

AbstractThis 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.