Design and performance of adaptive systems based on structured stochastic optimization strategies

The theory and design of linear adaptive filters based on FIR filter structures is well developed and widely applied in practice. However, the same is not true for more general classes of adaptive systems such as linear infinite impulse response adaptive filters (MR) and nonlinear adaptive systems. This situation results because both linear IIR structures and nonlinear structures tend to produce multi-modal error surfaces for which stochastic gradient optimization strategies may fail to reach the global minimum. After briefly discussing the state of the art in linear adaptive filtering, the attention of this paper is turned to IIR and nonlinear adaptive systems for potential use in echo cancellation, channel equalization, acoustic channel modeling, nonlinear prediction, and nonlinear system identification. Structured stochastic optimization algorithms that are effective on multimodal error surfaces are then introduced, with particular attention to the Particle Swarm Optimization (PSO) technique. The PSO algorithm is demonstrated on some representative IIR and nonlinear filter structures, and both performance and computational complexity are analyzed for these types of nonlinear systems.