Diversity Combination of Fading Signals with Unequal Mean Strengths

This paper compares several techniques of diversity combination without placing the usual restriction requiring the mean signal-to-noise ratios on the various diversity branches to be equal. The probability distribution of the postcombination SNR is calculated for various cases, and it is shown that the shape of this distribution curve is not greatly affected either by the choice of diversity technique or by reasonable unbalance in the mean SNR's on the various diversity branches. Various diversity techniques are compared by calculating the number of decibels by which transmitter power would have to be increased to achieve performance equivalent to that of the maximal-ratio combiner, which is the optimum. The same comparison is shown to hold, at the low SNR's that are of greatest practical interest, for a number of different types of fading, including Rayleigh fading of unequal mean strengths on the various branches, correlated Rayleigh fading, and certain nonRayleigh types. Constant-gain combination, which is a generalization of equalgain combination, is discussed. It is shown that the gains in the different diversity branches should be adjusted to make the noise powers equal before combination.