This paper analyzes the performance of direct-detection optical CDMA systems with single optical hard-limiter using equal-weight orthogonal (EWO) signaling. Moreover, this paper clarifies the basic structure and the performance of the system using time-shifted versions of optical orthogonal code (OOC's) as EWO signaling. The system assigns the time-shifted versions of OOC's to the transmission of bits "0" and "1," respectively. Thus, the system does not require dynamic estimation of the receiver threshold. The performance is analyzed under the Gaussian approximation of an avalanche photodiode (APD) output where the effects of APD noise, thermal noise and interference are included. From the theoretical analysis and numerical results, it is shown that the system has good performance without dynamic estimation of the receiver threshold.