In this paper, a cooperative cyclic-prefixed single carrier (CP-SC) system is studied and a scheme to improve its physical layer security is proposed. In particular, a distributed cyclic delay diversity (dCDD) scheme is employed and a deliberate interfering method is introduced, which degrades the signal-to-interference-plus-noise ratio (SINR) over the channels from a group of remote radio heads (RRHs) to an eaves dropper, while minimizing the signal-to-noise ratio loss over the channels from the RRHs to an intended user. This is obtained by selecting one RRH that acts as an interfering RRH and transmits an interfering artificial noise sequence to the eavesdropper. Through the use of the dCDD scheme, a channel that minimizes the receive SINR at the eavesdropper is selected for the interfering RRH. This choice enhances the secrecy rate of the CP-SC system. The system performance is evaluated by considering the secrecy outage probability and the probability of non-zero achievable secrecy rate, which are formulated in a closed-form analytical expression for identically and non-identically distributed frequency selective fading channels. Based on the proposed analytical framework, in addition, the diversity order of the system is studied. Monte Carlo simulations are employed to verify the analytical derivations for numerous system scenarios.