A major constraint in deployments of resource-limited networks is the energy consumption related to the battery lifetime of the network nodes. To this end, power efficient digital modulation techniques such as On-Off keying (OOK) are highly attractive. In this paper, a novel complete probabilistic description of the Direct Sequence - Coded Division Multiple Access (DS-CDMA) system with random signatures employing OOK modulation is presented. The system scenario considers simultaneously transmitting nodes in Rayleigh fading conditions. Numerical simulations are provided to support the derived results.