Performance evaluation of full-duplex AF relaying with direct link under residual self-interference

This paper investigates the error performance of a full-duplex (FD) amplify-and-forward (AF) single-relay system under the effect of residual self-interference whose variance is proportional to the λ-th power of the transmitted power (0≤λ ≤1). Our focus is on the cooperative FD linear relaying (LR) protocol that makes use of direct source-destination link. At first, a closed-form expression of the pairwise error probability (PEP) is derived for the considered system. This expression allows us to analyze the diversity behavior in high transmission power regions. Thanks to the use of the direct link, it is shown that the FD LR system can attain the same diversity function as its half-duplex (HD) counterpart as long as a suitable precoder is applied. Different from previous works that either ignore the direct link or treat it as a source of interference, a non-zero diversity order is thus achieved and the error floor behavior can be eliminated despite the existence of self-interference in FD. More interestingly, it is then demonstrated that transmitting a superposition of all symbols in HD mode maximizes the asymptotic coding gain. Although HD relaying is hence asymptotically optimal, simulations results reveal that FD is advantageous at practical bit error rate (BER) levels when λ is sufficiently small.