Convergence and Robustness Studies of Sign-Sign Adaptive Identifiers

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The sign-sign adaptive identifier is a computationally efficient variant of the standard identifier, in which the regressor and prediction error multiplicands of the update term of the LMS are replaced by their respective signum functions. Despite its wide use in a host of communications and signal processing applications, theoretical investigations into its properties are very few. Accordingly, the proposed project will conduct a theoretical study of convergence and robustness properties of this algorithm. The proposal outlines a number of performance differences between the sign-sign and the standard LMS. It emphasizes certain robustness enhancements enjoyed by the sign-sign relative to the standard LMS. It also demonstrates potential instability mechanisms within the sign-sign and highlights the need for developing excitation conditions for arresting such mechanisms and for ensuring the convergence of parameter estimates to their desired values. The non-gradient based nature of this algorithm, together with its intrinsic nonlinearity are expected to make its convergence and robustness analysis substantially different from those for traditional gradient based algorithms. The expected strategies for conducting such analyses are outlined, as also are the potential theoretical and practical benefits which this study is expected to carry. This research will attempt to derive a well founded theoretical basis for the sign-sign adaptive identifier which is an algorithm used to identity unknown signals. It is expected that such a theoretical basis will allow variations of the algorithm which can be employed in both signal processing and adaptive control.