Input–output identification of nonlinear channels using PSK, QAM and OFDM inputs

Nonparametric identification of baseband and passband complex Volterra systems excited by communication inputs (phase shift keying, PSK; quadrature amplitude modulation, QAM and OFDM) is considered. Closed form expressions are established using multivariate orthogonal polynomials and higher order statistics. First multivariate orthogonal polynomials are used for baseband and passband Volterra models driven by PSK and QAM inputs and closed form expressions are derived. For baseband Volterra models excited with i.i.d. complex Gaussian signals (OFDM), the general 2p+12p+1 order Volterra system is solved using cross-cumulants in time and frequency domain. An order recursive algorithm is presented for the latter case, that does not require a priori knowledge of the systems order. Performance is illustrated by simulations.