Diagonalizer for correlated or unbalanced diversity branches in Rayleigh or Rician fading channels and wireless communication

Due to the increasing interest in mobile/wireless communication, there has been a continuous research in antenna diversity to combat fading. And the model of correlated and unbalanced diversity branches reflects the real-world scenario. The diagonalizer is introduced here before the diversity branches are combined, which can transform the correlated and balanced branches to the uncorrelated and unbalanced ones, and vice versa. Also, the diagonalizer can be used to implement the optimum combining which is a quadratic combining for the correlated diversity branches. This paper assumes a generic case, in which noise and interference components are correlated with a correlation equal to or smaller than the correlation of signal components. Discussions on how to maximize diversity gains are made in various signal and noise conditions, and with different combining methods. The application of the technology presented in this paper is especially effective when the noise components have the same correlation as the signal components. This is the cases when interferences which come along with the desired signal are the main source of noise, such as the cases in CDMA systems and wireless networks, etc. The method described in this paper can act like a "filter" - to totally filter out the correlation among diversity branches in these cases.