Scalability Analysis of the Parallel Implementation of LMS and RLS Algorithms

The parallel implementation of the Least Mean Square (LMS) and Recursive Least Square (RLS) adaptive algorithms was investigated to study the scalability and the isoefficiency of these parallel implementations. The analysis includes deriving theoretical expressions for the computation and communication time for the parallel implementation of the adaptive algorithms. These expressions capture the characteristics of the adaptive algorithms for a particular architecture and could be used to assist in determining the optimum number of processors to be used for a particular problem size. The analysis also derives the isoefficiency function for the three adaptive algorithms. The isoefficiency function relates problem size to the number of processors required to maintain a system’s efficiency. It is used to gauge how a problem size should grow to maintain a fixed efficiency as the number of processors increases. The scalability analysis that was conducted for the parallel implementation of the LMS and RLS yields results which could help in the design of the algorithm on larger system for a given problem.