Tham khảo tài liệu 'advanced trends in wireless communications part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 130 Advanced Trends in Wireless Communications More specifically in Section 4 we have shown that the relays operate in a D-NC-F mode which means that they perform two error-prone operations i they use the DF protocol for relaying the received symbols and ii they combine the symbols received from the sources by using NC. The accurate computation of the APEPs in 20 requires that the error propagation caused by DF and NC operations at the relays are accurately quantified. DF and NC operations The effect of realistic source-to-relay channels As far as DF is concerned the error propagation of this relay protocol in two-hop relay networks has already been quantified in the literature. In particular in Hasna Alouini 2003 the following result is available. Given a two-hop source-to-relay-to-destination S-R-D wireless network the end-to-end . at destination D probability of error Psrd is given by PSRD PSR PRD - 2PSRPRD 21 where Psr and Prd are the error probabilities over the source-to-relay and relay-to-destination links respectively. By taking into account the analysis in Section 4 it can be readily proved that Psr o ựY PZSR 2and Prd o ựY hRD 2 . The average end-to-end probability of error Psrd can be computed from 10 and 11 and by taking into account that channel fading over the two links is uncorrelated. The final result from 21 is PSRD E PSRD PSR PRD - 2pSRP RD 2p - 2p2 22 Let us now consider the error propagation effect due to NC operations and caused by errors over the source-to-relay channels. In this book chapter NC when performed by the relays only foresees binary XOR operations see Section 3 . Thus we analyze the error propagation effect in this case only. The result is summarized in Proposition 1. Proposition 1. Let bs1 and bs2 be the bits emitted by two sources S1 and S2 see . 1 . Furthermore let bS1 and bS2 be the bits estimated at relay R see 3 after propagation through the wireless links S1-to-R and S2-to-R respectively. Finally let bR bS1 .
