Convergence properties of mixed-norm algorithms under general error criteria

The convergence properties of mixed-norm algorithms as i t applies to echo cancelers under general error criteria is derived for correlated and identically distributed inputs. The convergence analysis of this class of algorithms i s carried out using the linearization process of the error nonlinearities. Necessary and suficient conditions for convergence are derived for the independent input case. where f ( e ( k ) ) and g ( e ( k ) ) are the error nonlinearities, W N ~ and W F ~ are the true impulse responses of the nearend and far-end sections, respectively, and where P N and P F are the step sizes of the near-end and far-end sections, respectively. The error is &fined by e ( k ) = n ( k ) v L ( k ) x N ( k ) v > ( k ) x F ( k ) , ( 3 ) where n ( k ) is the additive noise.