In this paper, a cooperative single carrier system comprising multiple cooperating remote radio heads and a single interferer operating in the presence of co-existing line-of-sight and non-line-of-sight paths is investigated. Distributed cyclic delay diversity is employed as the transmit diversity scheme for cyclic-prefixed single carrier transmissions over independent but non-identically distributed frequency selective fading channels. The main focus of this paper is to investigate the achievable diversity gain in the interference-limited and noise-limited regions. In contrast to the outage probability in the noise-limited region, it is shown that the diversity gain is not achievable in the interference-limited region. To justify this finding, the outage probability is derived first, and then verified by link-level simulations.