Efficient System Tracking With Decomposable Graph-Structured Inputs and Application to Adaptive Equalization With Cyclostationary Inputs

This paper introduces the graph-structured recursive least squares (GS-RLS) algorithm, which is a very efficient means to track a linear time-varying system when the inputs to the system have structure that can be modeled using a decomposable Gaussian graphical model. For graphs with small clique sizes, it is shown that GS-RLS can achieve tracking performance very close to that of the conventional RLS algorithm for a fraction of the computational cost. In particular, after proving that the outputs of wide-sense stationary time-varying communication channels have graphical model structure if the inputs are cyclostationary, significant computational gains are realized for adaptive equalization of the time-varying underwater acoustic communication channel using the GS-RLS algorithm. This is verified using field data from the SPACE08 underwater acoustic communication experiment.