In this work, we present a novel adaptive filtering scheme that builds on and advances the method of joint iterative optimization (JIO) of reduced-rank filters proposed in [1]. The scheme applies the theory of error bounded set-membership filtering to both the adaptation of the bank of full-rank filters that form the projection matrix, and the reduced-rank adaptive filter that operates in the lower dimensional signal subspace. Derivation and interpretation of the proposed framework is given along with two normalized least-mean squares (NLMS) implementations where either the full projection matrix or its individual columns are adapted. The proposed algorithms are then applied to interference suppression in DS-CDMA systems and shown to exceed the performance of the conventional JIO NLMS while achieving a reduction in computational complexity.
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