Various approaches for incorporating prior system knowledge into adaptive filtering algorithms exist, e.g., using constrained adaptation. Moreover, also the basic setup of the adaptation problem, e.g., whether it is supervised or blind, can be considered as prior system knowledge. In this paper, we consider a systematic approach to incorporate such deterministic prior knowledge in broadband adaptive MIMO systems by optimizing the coefficients in arbitrary partly smooth manifolds. The resulting generic set of update equations explicitly shows all the available degrees of freedom for a top-down algorithm design. Using practically relevant examples, we show how both well-known and novel algorithms for various applications can be derived using the framework.
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