Generalized selection combining based on the log-likelihood ratio

We propose a generalized selection combining (GSC) scheme for binary signaling in which a subset of diversity branches providing the largest magnitude of log-likelihood ratio (LLR) are selected and combined. It is shown that the bit-error probability with maximum ratio combining (MRC) or square-law combining of L branches is identical to that with LLR-based GSC of L/2 branches. We also propose a simple, but suboptimal, GSC based on a noncoherent envelope detection and discuss its potential advantages over the conventional signal-to-noise-ratio-based GSC and MRC.