An enhanced Godard blind equalizer based on the analysis of transient phase

This dissertation proposes an enhanced version of the Godard blind equalizer also known as the constant modulus algorithm (CMA) among blind equalization algorithms, with faster convergence speed. By investigating the surface formed by the minimum points along the ray direction of constant modulus (CM) cost function, it is shown that the trajectory of equalizer coefficient vector asymptotically follows this surface near the global solution. Thus, it is observed that the behavior of equalizer output power is different from the behavior of intersymbol interference (ISI) during the transient phase in achieving the global solution. It is shown that the cause of slow convergence is closely related to the behavior of equalizer output power. For faster convergence, a gain stage is introduced after the equalizer. The role of the gain stage in the proposed method is to compensate for the power reduction caused by the tap update. Using the first order approximation on the prediction error function, the performance for the proposed method is analyzed to obtain the condition for dynamic convergence of the proposed algorithm. Comparing with the CMA, the performance improvement of the proposed CMA in the transient phase depends on the square of gain in the steady state. To resolve the problem that the added gain stage may result in bigger steady state mean-square error (MSE), the MSE is monitored during the transient phase. For comparison with the other modified CMA, methods including the CMA with the center tap initialization, the CMA with the gear shift method, and the CMA with the normalized step size, are introduced and analyzed. Through examples for these algorithms, under a simple channel, it is shown that 1) the performance analysis for the proposed CMA is valid, 2) the gain stage can be used well to keep the equalizer output power from being reduced excessively during the transient phase, and 3) the convergence speed of the proposed CMA is faster than those of the other CMA algorithms. i Copyright(c)2002 by Seoul National University Library. All rights reserved.(http://library.snu.ac.kr) 2003/08/24 13:15:22