Performance of Full-Duplex AF Relaying in the Presence of Residual Self-Interference

This paper investigates the error and diversity performances of full-duplex (FD) amplify-and-forward (AF) single-relay systems under the effect of residual self-interference. The variance of this interference is assumed to be proportional to the lambda-th power of the transmitted power (0 <= lambda <= 1). The study considers the cooperative linear relaying protocol with direct source-destination link and the dual-hop scheme without direct link, both under uncoded and coded frameworks. At first, closed-form pairwise error probability expressions are derived for the uncoded systems, which are then used to obtain tight bounds to the bit error rate (BER) of the coded systems. To shed an insight on the diversity behavior, asymptotic expressions at high transmission powers are also presented. Different from previous works that treat the direct link as interference, this paper shows that FD linear relaying systems with a suitable precoder can attain the same diversity function as their half-duplex (HD) counterparts. However, further analysis shows that HD orthogonal AF using a superposition constellation is asymptotically optimal in terms of maximum coding gain. In addition, it is shown that the diversity of FD dual-hop systems is a decreasing function of lambda and is equal to zero when lambda = 1. Although HD relaying is asymptotically optimal under the considered protocols and interference model, illustrative results show that FD relaying is advantageous at practical BER levels when lambda is sufficiently small.