A Method of Multi-Dimensional Blind Equalization
The blind equalization problem for the multi-channel data transmission is investigated. The algorithm is based on the principle of distribution matching, i.e., the total system must be transparent when both the transmitted signal and the equalizer output depend on the same distribution, where the transmitted signal is assumed to be IID sequence. The difficulty in its extension toward multi-dimensional cases is to reduce simultaneously cross-interference between channels and inter-symbol interference in each channel. The cost function, which measures the distance between the joint-distribution of equalizer output vector (z/sub k) and that of transmitted vector (a/sub k), is able to solve the difficulty. The proposed algorithm is closely related to the minimum entropy deconvolution (MED), whose cost function measures the distance from the Gaussian to the distribution of equalizer output. By extending kurtosis used in MED theory to multi-dimensional cases, we derive another cost function which appears to be equivalent to the first proposed cost function excepting power normalization.