A Sobolev Norm-Based Variational Approach to Companding for PAPR Reduction in OFDM Systems

In this paper we present a new approach to high-performance compander design to reduce the peak-to-average power ratio (PAPR) that typically occurs in orthogonal frequency division multiplexing (OFDM) systems. Whereas many current compander designs assume a parametric model for the form of the transformed Rayleigh amplitude distribution, we define a constrained optimization problem for the functional form of the transformed distribution. We determine an optimal distribution which minimally deviates from the Rayleigh distribution and use a Sobolev norm to quantify distance. Use of the Sobolev norm imposes smoothness constraints on the transformed distribution, which are associated with lower out-of-band interference levels. We incorporate Lagrange multipliers into the problem formulation to enforce the constant power and probability density function constraints. We solve the constrained optimization problem using techniques from the Calculus of Variations and discuss compander and decompander design. We investigate the effect of incorporating derivative information, into the optimization formulation, on compander performance. We demonstrate compander performance through numerical simulation and compare compander performance to performance from a state-of-the-art variational compander which does not use derivative information in the formulation. We demonstrate performance improvements in out-of-band power rejection using the new compander.