This paper presents non-orthogonal multiple access (NOMA)-based spectrum sharing scheme for cooperative underlay cognitive radio (CR) wherein the cell-edge primary receiver (CE-PR) can decode the symbols in every time slot by exploiting cooperative multiplexing. In the proposed scheme, the secondary receiver is employed as a cooperative node to achieve a full-duplexing rate at the primary network. Due to this fact and the absence of interference from the primary network, the performance of the secondary network suffers only from self-loop interference (SI). On the other hand, since the secondary transmitter (ST) is not transmitting simultaneously with the primary transmitter, CE-PR can receive the symbol from the direct link without ST interference. In this paper, we derive the closed-form expression for computing the outage probability and the sum rate of the proposed system under imperfect successive interference cancellation (SIC). For comparison purposes, we present the rate and outage performance of the orthogonal multiple access (OMA)-based underlay CR.