Abstract: By expressing the decision variables of transmission symbols in time-varying multipath Rayleigh fading channels as the Gaussian quadratic vector form, we derive the analytic expression for its characteristic function as a function of the eigenvalues of the weighted covariance matrix. Therefore, the matched filter bound for such channels can be expressed as the sum of the coefficients corresponding to the negative eigenvalues in the partial fraction expansion of the characteristic function. We further compare in matched filtering performance several modulation pulses in time-varying multipath Rayleigh fading channels, with the result that the rectangular pulse can achieve the best time and frequency diversity.

Key words: time-varying multipath Rayleigh fading channels, characteristic function, matched filter bound