  In a distributed network environment, the diffusion-least mean squares (LMS)
algorithm gives faster convergence than the original LMS algorithm. It has also
been observed that, the diffusion-LMS generally outperforms other distributed
LMS algorithms like spatial LMS and incremental LMS. However, both the original
LMS and diffusion-LMS are not applicable in non-linear environments where data
may not be linearly separable. A variant of LMS called kernel-LMS (KLMS) has
been proposed in the literature for such non-linearities. In this paper, we
propose kernelised version of diffusion-LMS for non-linear distributed
environments. Simulations show that the proposed approach has superior
convergence as compared to algorithms of the same genre. We also introduce a
technique to predict the transient and steady-state behaviour of the proposed
algorithm. The techniques proposed in this work (or algorithms of same genre)
can be easily extended to distributed parameter estimation applications like
cooperative spectrum sensing and massive multiple input multiple output (MIMO)
receiver design which are potential components for 5G communication systems.
