On gradient adaptation with unit-norm constraints

In this correspondence, we describe gradient-based adaptive algorithms within parameter spaces that are specified by ||w||=1, where ||/spl middot/|| is any vector norm. We provide several algorithm forms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for L/sub 2/-norm-constrained optimization tasks. Simulations showing the performance of the techniques for independent component analysis are provided.