In this paper, we present a capacity analysis for broadband power line communication (PLC) channels, impaired by the Bernoulli-Gaussian impulsive noise, exploiting both orthogonal frequency division multiplexing (OFDM) and singlecarrier frequency-domain equalisation (SC-FDE) techniques. First, we investigate point-to-point communications and formulate the continuous signal model for OFDM and SC-FDE techniques in PLC environments and find the tight bounds derived for differential entropy of the non-Gaussian noise samples. Capacity bounds and a certain capacity result for pointto-point PLC systems are also computed. Then, we analyse the capacity in the presence of a relay terminal between the transmitter and the receiver. In this part, we assume correlated noises between the relay and the receiver and derive general upper bound and achievable rate using partial decode-and-forward coding strategy for PLC channels. We also show that the obtained bounds coincide in degraded and reversely degraded special cases. Finally, using two statistical divergences, we compare the distances of the Bernoulli-Gaussian and Middleton class A noise models from the normal distribution of their background part and show that the Middleton class A noise is nearer to the Gaussian background noise than the Bernoulli-Gaussian. Therefore, the capacity curve for Middleton class A noise is between the capacity for the Gaussian background noise and the obtained capacity for the Bernoulli-Gaussian model. The obtained capacity theorems are also illustrated numerically.
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.
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