Performance analysis of hierarchical selection diversity combining in Rayleigh fading

In a previous work, a hierarchical selection diversity scheme (HSD) was proposed as a cost-effective means of extracting a high diversity gain out of a large antenna array. To achieve this, the array is split up into a number of groups and the antenna having the best instantaneous SNR in each group is selected for further processing. The resulting selected set then undergoes maximal-ratio combining. It was shown that this scheme with a group size of 2 yields a performance within a few dBs of that of full maximal-ratio combining of the array, yet requires only half the RF chains. In this paper, derivations are provided for the outage probability with a group size of 2, for the output SNR distribution for a group size of 3, and error rate results are provided for arbitrary group sizes.