Generalized kurtosis and applications in blind equalization of MIMO channels

Recently, the problem of blind equalization of multiple-input multiple-output (MIMO) channels has received much attention from the communications and signal processing communities. Several methods proposed to solve this problem involve computing the kurtosis of the components of the observed output vector sequence. In this paper, we generalize the notion of kurtosis to vector sequences by proposing a definition for a kurtosis matrix of a random vector. It is shown that there are many analogies between our kurtosis matrix and the classical scalar kurtosis. We then use this matrix to develop a necessary condition for blind equalization of MIMO channels. Future work will include the development of a sufficient condition for equalization.