Graph Filter Design for Distributed Network Processing: A Comparison between Adaptive Algorithms

Graph filters (GFs) have attracted great interest since they can be directly implemented in a diffused way. Thus it is interesting to investigate GFs to implement signal processing operations in a distributed manner. However, in most GF models, the input signals are assumed to be time-invariant, static, or change at a very low rate. In addition to that, the GF coefficients are usually set to be node-invariant, i.e. the same for all the nodes. Yet, in general, the input signals may evolve with time and the underlying GF may have parameters dependent on the nodes. Therefore, in this paper, we consider dynamic input signals and both types of GF coefficients, node-variant, i.e. vary on different nodes, and node-invariant. Then, we apply LMS and RLS algorithms for GF design, along with two others called adapt-then-combine (ATC) and combined RLS (CRLS) to estimate the GF coefficients. We study and compare the performance of the algorithms and show that in the case of node-invariant GF coefficients, CRLS gives the best performance with lowest mean-square-displacement (MSD), whereas, for node-variant case, RLS represents the best results. The effect of bias in the input signal has also been examined.