System modeling and design using genetic programming

In this paper we describe nonlinear system modeling and design using genetic programming (GP). In order to demonstrate the ability of GP to design complex systems, we first present a novel scheme called improved least squares genetic program (ILS-GP) that attempts to reconstruct the functional form of a nonlinear dynamical system from its noisy time series measurements. ILS-GP augments the structural search ability of GP with a novel parameter estimation scheme called improved least squares designed specifically to eliminate bias in parameter estimates of the nonlinear dynamical system in the presence of measurement noise. We use different test chaotic systems and real-life radar sea scattered signals to demonstrate the effectiveness of the ILS-GP approach in reconstructing nonlinear systems. Having shown the ability of GP to reconstruct complex systems from their time series measurements, we apply GP to the reverse problem of constructing optimal systems for generating specific sequences called spreading codes in CDMA communications. Using different approaches including correlation properties and the bit error rate, we use the proposed GP approach to design chaotic piecewise maps that generate optimal spreading codes in complicated communication environments such as multi-path. Based on computer simulations, we have shown improved performance of the GP-generated maps when compared to the other approaches including the standard Gold code.