In this paper, a new transmit diversity scheme for cooperative non-orthogonal multiple access (NOMA) is proposed without perfect channel state information at the transmitter (CSIT). To support two users under a near-far user pairing constraint, a distributed cyclic delay diversity (dCDD) scheme is adjusted into NOMA by dividing a set of remote radio heads (RRHs) into two groups for multiple cyclic-prefixed single carrier transmissions. Using only a limited channel relevant information needed to make dCDD work, a new RRH assignment and power allocation mechanism is proposed. After then, closed-form expressions for the rates of two users achieved by the proposed RRH assignment and power allocation mechanism are derived. For various scenarios, link-level simulations verify that superior rates can be achieved by NOMA with dCDD over the traditional orthogonal multiple access with dCDD.