On the Symbol Error Rate and Diversity Gain Region of the Relay-Assisted Z-channel

Abstract

Interference forwarding in a Z-channel makes interference stronger, which in turn enables usage of simple detectors like successive interference canceler (SIC) at interference-limited destination. In this work, the following protocols with SIC at the interference-limited destination are investigated: direct transmission ( $SIC_{Direct}$ ), half-duplex decode-and-forward ( $SIC_{DF}$ ), and half-duplex amplify-and-forward ( $SIC_{AF}$ ) protocols. The achievable diversity orders of these protocols using M-PAM and M-QAM modulation are obtained. Moreover, minimum required exponential orders of the average received signal powers at the relay and interference-limited destination to restore full diversity are presented. The $SIC_{AF}$ and $SIC_{DF}$ protocols are shown to achieve the same diversity order as that of the orthogonal transmission scheme while achieving better spectral efficiency than the orthogonal transmission. Closed-form expressions for the achievable diversity gain regions (DGRs) with the $SIC_{Direct}$ , $SIC_{DF}$ , and $SIC_{AF}$ protocols are derived. Selective decode-and-forward with SIC ( $SIC_{SDF}$ ) is also considered. The multiplexing gain regions and the interference levels where the $SIC_{AF}$ and $SIC_{SDF}$ protocols achieve better DGR than the $SIC_{Direct}$ protocol are obtained.