Transform methods of PAM signals for asymmetric distribution in 3rd-order blind equalizer

In this paper, we have considered the 3rd order blind equalizer using symmetric to asymmetric transforms and asymmetric to symmetric transforms of PAM signals by the square root operation and reciprocal operation. The purposes of these transforms and 3rd order blind equalizations are (i) better mean square error (MSE) performances with less computational complexities than 4th order blind equalizers and (ii) real time operations are required for estimating 3rd order cumulants. At the receiver square operation and reciprocal observation are required for recovering the asymmetrically transformed signals after equalization. As a result of computer simulation, transform methods with reciprocal and square root operations are better than the transform method with the natural logarithmic operation by about 8 dB maximum in MSE at specific K, compression factor. The computational complexities of the 3rd order method are about a half that of the 4th order method. We discuss the importance of skewness at small values and the performance of the blind equalizer.