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Throughout this study, a novel network model for massive machine-type communications (mMTC) is proposed using a compressive sensing (CS) algorithm and a non-orthogonal multiple access (NOMA) scheme. Further, physical-layer security (PLS) is applied in this network to provide secure communication. We first assume that all the legitimate nodes operate in full-duplex mode; then, an artificial noise (AN) signal is emitted while receiving the signal from the head node to confuse eavesdroppers (Eve). A convex optimization tool is used to detect the active number of nodes in the proposed network using a sparsity-aware maximum a posteriori (S-MAP) detection algorithm. The sensing-aided secrecy sum rate of the proposed network is analyzed and compared with the sum rate of the network without sensing, and the closed-form expression of the secrecy outage probability of the proposed mMTC network is derived. Finally, our numerical results demonstrate the impact of an active sensing algorithm in the proposed mMTC network; improvement in the secrecy outage of the proposed network is achieved through increasing the distance of the Eve node.