Analysis of sigmoid-based blind equalizer algorithms

This Paper presents sigmoid-based modified decision-directed algorithm (MDDA) and modified decision-directed modulus algorithm (MDDMA) to optimize the algorithm behavior within a real-time environment. Using the sigmoid function instead of the signum function for this group of algorithms leads to a decreasing of the equalizer length, enhancement of the step size parameter (μ), optimization of the bit error rate (BER) and to a reduction of the mean square error (MSE). Applying a sigmoid function results in a nonlinear soft decision of the equalizer output compared to the signum function which represents a nonlinear hard decision. Additional to the simulation results, both algorithms are process-optimized for real-time baseband transmission in a digital signal processor (DSP) test-bed for differential modulations schemes. All presented BER simulation results are supported by BER measurements achieved with the laboratory test-bed. The character of the sigmoid-based nonlinearity can be described as a loupe function to increase the operating range of a blind equalizer for fixed step-size parameter.