Blind equalization using third-order moments

Abstract: The use of third-order moments in blind linear equalization has been studied with emphasis on their performance in on-line methods of low complexity. Blind equalization has widespread use in areas such as digital communications, acoustics, geophysical exploration, image processing and general measurement problems. The objective is to recover a desired, unknown source signal from distorted observations using a linear filter. In contrast to classical methods of deconvolution or trained equalization, no model of the distorting system or temporal observations of the source are assumed. Instead, knowledge of the higher-order source statistics are exploited to find an appropriate equalizer setting through some iterative numerical procedure. The application field and research area have traditionally focused on methods based on fourth-order statistics. Examples are various kurtosis-maximization approaches and the widely used constant modulus algorithm (CMA). While qualifying for blind methods, third-order statisticshave attracted less attention, mainly due to the reason that they can only be used when the source signal is asymmetric, i.e. when the probability density is skewed. As a consequence of the more restricted usability of third-order methods, mostly experimental research results can be found, with little explanation for their performance. This work provides analytic and numerical results motivating why third-order methods should generally be chosen over their fourth-order counterparts when possible. It is shown that they possess improved convergence properties and robustness to noise, and that they lend themselves to efficient implementation on digital real-time hardware. These combined features make third-order methods an interesting option for on-line blind equalization.