This paper aims to extend the proportionate adaptation concept to the design of a class of diffusion normalised subband adaptive filter (DNSAF) algorithms. This leads to four extensions of the algorithm associated with different step-size variation, namely, diffusion proportionate normalised subband adaptive filter (DPNSAF), diffusion µ-law PNSAF (DMPNSAF), diffusion improved PNSAF (DIPNSAF) and diffusion improved IPNSAF (DIIPNSAF). Subsequently, steady-state performance, stability conditions and computational complexity of the proposed algorithms are investigated. For each extension the performance has been evaluated using both real and simulated data, where the outcomes demonstrate the accuracy of the theoretical expressions and effectiveness of the proposed algorithms.

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