Estimation of cubic nonlinear bandpass channels in orthogonal frequency-division multiplexing systems

Modeling and compensation of nonlinear communication channels has long been an important research topic in digital communications. A nonlinear bandpass channel is commonly modeled by a baseband equivalent Volterra series which relates the complex envelopes of the channel input and output. In this paper, we propose a novel method to estimate the frequency-domain baseband equivalent Volterra kernels of cubically nonlinear bandpass channels in orthogonal frequencydivision multiplexing (OFDM) systems. We recognize that the input signal for an OFDM system employing QAM or PSK modulations satisfies the properties of a kind of random multisine signal. By exploring the higher-order auto-moment spectra of the random multisine signal, a computationally efficient algorithm for determining the frequency-domain baseband equivalent Volterra kernels is derived. The obtained kernel estimates are optimal in the minimum mean square error (MMSE) sense. The proposed method can be used to estimate nonlinear bandpass channels for OFDM systems employing pure QAMs, pure PSKs, or a mixture of QAMs and PSKs. The effectiveness of the proposed method is demonstrated by applying it to estimate the nonlinear bandpass channel of an example OFDM system. Nonlinear channel compensators based on the Volterra model can benefit from the proposed method.