While linear approximations and models possess simplicity and tractability in analysis, most real life problems entail nonlinear effects. Nonlinear system of current interest in signal processing and communications are encountered with satellite links, high-speed telephone channels, power amplifiers, magnetic and optical recording systems. This research is exploring novel techniques for identification, performance analysis, and mitigation of nonlinear systems. The goal is to use state-of-the-art statistical signal processing tools to analyze long-standing issues in nonlinear modeling and applications to tele- communications problems. The present approach is taking a fresh look at the traditional Volterra model and exploiting carefully designed cyclostationary inputs that result in closed-form kernel expressions with input-output data. Such solutions will apply to finite memory Volterra models of any order, reduce computational complexity and noise effects even with relatively short data records, and allow for analytical performance evaluation using variance expressions. The investigator plans to simulate and test the resulting algorithms using real data received from satellite links where amplifiers are driven to the nonlinear saturation region. She is also studying blind nonlinear Volterra system identification that relies on single or multi-sensor data only. The potential of blind nonlinear channel estimation and equalization is of paramount importance when no training inputs are available, or when new communicators join a multiport broadcast and transmission cannot be interrupted for training.
