Tracking model of an adaptive lattice filter for a linear chirp FM signal in noise

The paper studies the behavior of the partial correlation (PARCOR) coefficients and the output misadjustment of the stochastic gradient adaptive lattice filter in response to a complex linear chirp FM signal in white Gaussian noise. Analytic expressions for the optimal PARCOR coefficients of the filter are derived. Analytic as well as iterative models for a three-stage filter are also derived. The analytic expressions show that the tracking and convergence properties of the filter are separate phenomena. Simulation results also show that the spectral contents of the PARCOR coefficients for the stochastic gradient update algorithm consist of a stationary and a linearly swept component. A single-stage model is developed to explain this behavior. Finally, output misadjustment plots for the filter show that an optimum value for the forgetting factor can be obtained to minimize the misadjustment, but the value required to achieve local minimum misadjustment varies with each stage of the filter. It is shown that in applications where the input has a high signal-to-noise ratio (SNR), the misadjustment decreases rapidly at each successive stage, thus implying that relatively short filter lengths are sufficient to provide effective tracking