Performance Analysis of Selection Combining of Signals With Different Modulation Levels in Cooperative Communications

Cooperative relaying introduces spatial diversity through the creation of a virtual antenna array. The vast majority of research in bit-error-rate (BER) performance analysis of selection-combining (SC) schemes used in digital cooperative relaying assumes the modulation level used by both the source and the relay to be the same. This assumption does not necessarily hold when adaptive modulation is implemented. In conventional SC, the branch with the highest signal-to-noise ratio (SNR) is chosen; we refer to this scheme as SNR-based SC (SNR-SC). However, when different modulation levels are employed, the branch that has the maximum SNR may not necessarily be the most reliable branch due to different error-resistance capabilities of the modulation levels. Consequently, the BER-based SC (BER-SC) is a better SC scheme. In BER-SC, the receiver calculates the BER for each branch (using the SNR and the modulation level) and then decodes the signal from the branch that has the minimum BER. In this paper, we provide BER performance analysis for both BER-SC and SNR-SC and show that BER-SC outperforms SNR-SC, with very comparable complexity. Moreover, we analytically quantify the gain achieved by using BER-SC over SNR-SC through asymptotic approximation. We note that BER-SC and SNR-SC schemes are identical when the received signals belong to the same modulation level.