A combinatorial analysis and a closed-form analytical expression for the signal to third-order distortion ratio in OFDM signals through smooth memoryless nonlinearity

In this paper we present a combinatorial analysis that explicitly exposes the exact number, weight and relative phase contributions of individual in-band signal subcarriers, for the in-band nonlinear distortion, experienced by a specific subcarrier in a nonlinearly distorted multicarrier Orthogonal Frequency Division Multiplex (OFDM) signal. This analysis is based on a discrete model of the passband signal and a polynomial smooth memoryless model of the nonlinearity. A closed-form analytical formula for the in-band intermodulation distortion is derived, which precisely quantifies the Signal to Third-Order Distortion Ratio for each subcarrier, permitting the calculation of the individual subcarrier and the overall OFDM signal Bit Error Rate (BER) performance. The motivation is the development of a simple and accurate analytical tool for the characterization of the nonlinear distortion performance of systems that use amplification for antenna received DVB-T signals. Our approach follows a straightforward combinatorial analysis and requires minimum signal and nonlinearity information.