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 square root operation and reciprocal operation. The purposes of these transforms and 3rd order blind equalizations are i) the better performances as MSE with less computational complexities than 4th order blind equalizer and ii) the real time operations for estimating 3rd order cumulants. At the receiver, square operation and reciprocal operation are required for recovering the asymmetrically transformed signals after equalization. As a result of computer simulation, transform methods with the reciprocal and square root operations are better than transforms method with natural logarithmic operation as 8 dB maximum in MSE at specific K, compression factor. The computational complexities of 3rd order method are about a half to that of 4th order method. Also we have found the importance of skewness at small values as a role of the performance for blind equalizer.