Identification of Volterra kernels for nonlinear communication systems with OFDM inputs

The orthogonal frequency-division multiplexing (OFDM) is a multicarrier modulation scheme developed for wideband communication applications. An inherent problem of the OFDM signal is that it could suffer from nonlinearities of power amplifiers in a communication link. For a nonlinear bandpass channel, the complex envelopes of its input and output are often related by a complex baseband equivalent Volterra series. To characterize the nonlinear channel, identification of the Volterra kernels is required. Many Volterra kernel identification methods found in the literature are applicable to systems with relatively low order nonlinearities. However, they might not be easily extendable to cases with higher-order nonlinearities in a straightforward manner. In this paper, a closed-form solution of the frequency-domain baseband equivalent Volterra kernels for nonlinear channels up to the 5th order is derived. The derivation is achieved by taking advantage of the higher-order auto-moment spectral properties of OFDM signals. The proposed method is computationally efficient and can obtain optimal minimum mean square error (MMSE) estimates of the Volterra kernels. The correctness of the derived formula is justified by computer simulation.