On the SNR Penalties of Ideal and Non-ideal Subset Diversity Systems

Subset diversity (SSD) techniques, which select and combine the signals from a subset of the available diversity branches, are important for practical wireless systems. This paper characterizes the performance loss, or signal-to-noise ratio (SNR) penalty, of one SSD system with respect to another. Both ideal and non-ideal channel estimation are considered, and the analysis is valid for the important case of arbitrary two-dimensional signal constellations. Expressions are given for the asymptotic SNR penalty, for both small and large SNR, for all the comparisons considered. Additionally, we develop bounds and approximations to quantify the performance of one system in terms of another for all SNRs of interest. Furthermore, for some signal constellations, we derive the exact SNR penalty of a non-ideal system with respect to an ideal system, as well as the exact penalty associated with two non-ideal systems with varying degrees of estimation energy. The SNR penalty enables the assessment of system sensitivity to channel estimation energy, combining architecture, and signal constellation.