We propose a new differential maximum-likelihood (DML) combiner for noncoherent detection of the differential amplify-and-forward (D-AF) relaying system in the time-selective channel. The weights are computed based on both the average channel quality and the correlation coefficient of the direct and relay channels. Moreover, we derive a closed-form approximate expression for the average bit error rate (BER), which is applicable to any single-relay D-AF system with fixed weights. Both theoretical and simulated results are presented to show that the time-selective nature of the underlying channels tends to reduce the diversity gains at the low-signal-to-noise-ratio (SNR) region, resulting in an asymptotic BER floor at the high-SNR region. Moreover, the proposed DML combiner is capable of providing significant BER improvements compared with the conventional differential detection (CDD) and selection-combining (SC) schemes.
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