Effects of correlated fading on level crossing rates and average fade durations with predetection diversity reception

General expressions for the level crossing rate (LCR) and average fade duration (AFD) are obtained for several diversity combining schemes employing two-branch predetection reception of correlated Rayleigh fading signals. These expressions are obtained from joint and conditional probability density functions (PDFs) of the received signals, and lead to a unified treatment. This simplified method contrasts with the characteristic function approach used in previous investigations. Numerical results are presented for a space-diversity system using horizontally spaced antennas at a mobile station. It is shown that while the angle between the antenna axis and the direction of vehicle motion does not appear in the cumulative distribution function (CDF) of the combined output signal envelopes, it affects the LCR and AFD when the two fading signals are correlated. When the two antennas parallel with the direction of vehicle motion are used, the LCR can be reduced below the value obtainable from signals which fade independently. When the two antennas are perpendicular to the direction of vehicle motion, the AFD is loosely dependent on the antenna spacing and, provided the antenna spacing is not too small, is approximately half that for the no-diversity case.