Transform domain filtering in incremental and diffusion strategies over distributed networks

Abstract

We analyse incremental and diffusion co-operative schemes in which nodes share information to some neighbour nodes in order to estimate desired parameter of interest locally in the presence of noise. Each node works as an adaptive filter and having its own learning ability. In incremental co-operative fashion a node takes information from previous node and after local estimation the information is sent to next node whereas in diffusion the input is taken from various nodes so that after each iteration the behaviour of distributed network is observed. We employ LMS structure for updating the observations. The convergence performance and computational complexity of LMS-filter is very important consideration for the point of view of speed boost and cost reduction. The convergence performance of a filter depends on eigenvalue spread of covariance matrix of input data or in other words inversely proportional to the eigenvalue spread of the input data. If input data is de-correlated the eigenvalue spread is less and if input data is correlated the eigenvalue spread is more. Transform domain filter has data de-correlation properties of transforms like DCT & DFT. The data de-correlation by the unitary transforms is depends on the orthogonal property of individual transform. Hence we get improved convergence performance by applying transform domain to input data followed by power normalization of input data. If the input data is fully de-correlated the covariance matrix of input data is proportional to the identity matrix.