Second-order statistics blind MIMO-FIR channel equalization for antenna array-based wireless communications systems

A theoretic framework on blind MIMO-FlR channel equalization by use of SOS (second-order statistics) is established. First, a sufficient condition is given on the autocorrelations of source signals. Under this condition, it is guaranteed that an MIMO-FIR channel is equalized up to some scalar factors and some delays if, and only if, some SOS of the composite output signals are the same as that of the source signals. Subsequently, the concept of pre-filters are introduced to convert white sources, which do not satisfy this sufficient condition, into color ones that do satisfy it. Based on the sufficient condition and the pre-filters, a set of theorems are developed for blind MIMO-FIR channel equalization, which only use the SOS of the received signals. Finally, a computer simulation is conducted to verify this theory. The theory and methods can be applied to antenna array-based wireless communications systems for high bandwidth efficiency.