Single-carrier (SC) block transmission  is an efficient scheme in multipath channels. With frequency-domain equalization, SC block transmission avoids complex time-domain equalization. There are also several systems proposed that combine SC-FDE with code-division multiple access (CDMA). However, unlike conventional direct-sequence (DS) CDMA, the present CDMA systems with FDE may be not suitable for asynchronous users, for lack of a signal model that could suitably express the despread signal in frequency domain. In this paper, we propose a novel architecture of SC block transmission DS-CDMA that can be applied for asynchronous users. A new signal model is derived that represents spreading, channel effect, and despreading as a series of circular convolutions. This signal model helps in deriving a new frequency-domain minimum mean-square error (MMSE) equalization algorithm for SC block transmission CDMA. Based on the proposed signal model, we also propose a simple channel estimation algorithm. Our architecture and signal model can be applied for further development of multi-user detection algorithms.