The Effect of Unbalanced Branches on the Performance of Diversity Receivers for Urban Fixed Wireless Links

Diversity techniques can be very effective against fading. For fixed wireless terminals, antenna diversity increases spatial coverage by reducing the likelihood of all antennas being at a faded location. At the same time, temporal fade depth is reduced, as time variations are normally uncorrelated for the antennas. The analysis of temporal fade in fixed wireless applications must take into account that the standard assumption made in mobile applications, namely equal average power across the diversity branches, is no longer justified, as a given antenna may be at a faded location for an extended time. In this paper we quantify the benefits of diversity receivers for fixed wireless links in terms of reductions in temporal fluctuation and outages, including the effect of power unbalance among diversity branches which is typical for these links. We specifically consider the case where the time varying multipath fade components are independent but identically distributed random processes for all branches, while due to spatial fades, the time invariant components may be different. A statistical description that includes the average level crossing rate (LCR) of the output signal of a maximal ratio combiner is derived in closed form. Simplified expressions, applicable for the case of links with high Ricean X-factors, as occurs in fixed wireless, are derived for both maximal ratio and equal gain combining. It was found that the combiner output statistics essentially depend on the value of sum of the branch K-factors, with the number of branches having virtually no effect. Extensive measurements at 3.5 GHz are used to compare, and found to match well, the theoretical expressions derived in this work. The results are useful for link design, by providing theoretical tools and empirical data for the calculation of the fade margin reduction and fade duration that results from the use of diversity combiners in the case of fixed wireless links with unequal power across the diversi- ty branches.