COMPUTATIONAL COMPLEXITY ANALYSES OF ADAPTIVE EQUALIZATION ALGORITHMS IN LINEARLY DISPERSED CHANNEL SYSTEMS

This paper presents a framework for assessing the complexity of adaptive equalizationalgorithms in a linearly dispersive channel that produces unknown distortion. Threealgorithms are investigated including the Least Mean Squares (LMS), Recursive LeastSquares (RLS), and Recursive Least Squares Lattice (RLSL) algorithms with respect to themean square error (MSE) and the sample convergence speed. The simulation resultsreveal several insights: In terms of channel dispersion, the MSE performance of the LMSdeteriorates by up to 40 % when the channel eigenvalue spread doubles. In addition, theconvergence speed of LMS reduces by up to 50% for the same increase in channel spreadand is invariant to the filter order. The same observation is applicable to the RLS andRLSL algorithms. The RLS algorithm gives the highest MSE performance for practicalsignal to noise ratio (SNR) ranges; It outperforms the LMS scheme by up to 50% and theRLSL by up to 20%. In terms of convergence speed, the RLS algorithm converges fastest ataround 100 data samples and the LMS is the slowest requiring 800 samples while theRLSL algorithm requires up to 200 samples to converge. Observation of other metrics ofthe RLS and RLSL algorithms including the last tap weight coefficient of the LMS/RLS andthe steady-state regression coefficient of the RLSL reveal the symmetry and asymmetry intheir statistics respectively. The choice of the equalization algorithm to be used depends ona number of design tradeoffs including the propagation environment, the SNR sensitivity,and the computational power.