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In this paper, it is proposed to use asymmetric complex signaling in full-duplex decode-and-forward single antenna relay channels in order to eliminate the self-interference signal and increase the throughput. Specifically, the relay system considered in this paper is as follows: the source has a transmit weight; the relay has an Rx processing whose operation is an inner product between the received signal and a weight; the relay has a transmit weight as well; the destination has a receive weight. The objective is to find the optimum weights to increase the smaller SNR between source-relay and relay-destination under the constraint of perfect self-interference nulling. We convert the complex variable into a 2-dimensional real vector. As a consequence, the problem becomes a joint vector optimization problem. The simulation result shows that the proposed signalling achieves higher rate than the conventional full-duplex relay.