An equalizer initialization technique for least mean squares (LMS) algorithm, which can equalize frequency selective multiple input multiple output (MIMO) channels, is presented and analyzed. The proposed method conducts an initial convergence step for superior training prior to running the LMS algorithm. This approach raises the training performance while the complexity of the LMS algorithm, which is known as the simplest training algorithm, is almost the same. The proposed technique is analyzed for the initial convergence and simulated for a possible single carrier MIMO application in single carrier (SC) IEEE802.16-2004 standards. The obtained performance after coding approximates the performance of the recursive least squares (RLS) algorithm as it is presented for 33 and 55 MIMO for comparisons.

Because of the fact that mobile communication channel changes by time, it is necessary to employ adaptive channel equalizers in order to combat the distorting effects of the channel. Least Mean Squares (LMS) algorithm is one of the most popular channel equalization algorithms and is preferred over other algorithms such as the Recursive Least Squares (RLS) and Maximum Likelihood Sequence Estimation (MLSE) when simplicity is the dominant decision factor. However, LMS algorithm suffers from poor performance and convergence speed within the training period specified by most of the standards. The aim of this study is to improve the convergence speed and performance of the LMS algorithm by adjusting the step size using fuzzy logic. The proposed method is compared with the Channel Matched Filter-Decision Feedback Equalizer (CMF-DFE) [1] which provides multi path propagation diversity by collecting the energy in the channel, Minimum Mean Square Error-Decision Feedback Equalizer (MMSE-DFE) [2] which is one of the most successful equalizers for the data packet transmission, normalized LMS-DFE (N-LMS-DFE) [3] , variable step size (VSS) LMS-DFE [4] , fuzzy LMS-DFE [5],[6] and RLS-DFE [7] . The obtained simulation results using HIPERLAN/1 standards have demonstrated that the proposed LMS-DFE algorithm based on fuzzy logic has considerably better performance than others.