In this paper we present the performance analysis of a novel channel assignment scheme where two non-cooperative independent users simultaneously communicate with their destination through a single relay by using only two frequency channels. The analytic derivation of the probability of symbol error for two main relay techniques will be provided, namely Amplify-and-Forward (AF) and Decode-and-Forward (DF). As shown by the obtained results, our switched-frequency approach results in a model that can achieve full- diversity by means of maximum-likelihood decoding at the receiver. Our results are especially important in the DF case, since in traditional techniques (such as half-duplex two-time slot approaches) two sources si-multaneously transmit on the same channel through the first time slot, which necessitates some sort of su-perposition coding. However, since in our scheme both users transmit over orthogonal channels, such a coding scheme is not required. In addition, it is shown that the DF approach based on our novel channel assign-ment scheme outperforms the AF scheme, especially in scenarios where the relay is closer to the receiver.