A Modified Barrett-Lampard Expansion and Its Application to Bandpass Nonlinearities with Both AM-AM and AM-PM Conversion

A two-dimensional Barrett-Lampard expansion is developed to handle two-dimensional nonlinear systems with random Gaussian inputs. The theory is applied to the problem of evaluating the mean signal and the inphase and quadrature noise correlation functions at the output of a TWT nonlinearity exhibiting arbitrary AM-AM and AM-PM characteristics, when the input consists of a narrow-band signal and Gaussian noise. As a specialized application, the classical problem of determining the coherent and incoherent noise correlation functions at the output of a power-law bandpass nonlinearity is also considered. The results are of interest in assessing the performance of coherent satellite communication channels. The theory developed is accompanied by numerical examples of practical interest.