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In this paper, we consider an uplink multiple-antenna code-division multiple-access (CDMA) system linking several multiple-antenna mobile users to one multiple-antenna base station. For this system, a constrained third-order tensor decomposition is introduced for modeling the multiple-antenna transmitter as well as the received signal. The constrained structure of the proposed tensor decomposition is characterized by two constraint matrices that have a meaningful physical interpretation in our context. They can be viewed as canonical allocation matrices that define the allocation of users' data streams and spreading codes to the transmit antennas. The distinguishing features of the proposed tensor modeling with respect to the already existing tensor-based CDMA models are: i) it copes with multiple transmit antennas and spreading codes per user and ii) it models several spatial spreading/multiplexing schemes with multiple spreading codes by controlling the constrained structure of the tensor signal model. A systematic design procedure for the canonical allocation matrices leading to a unique blind symbol (or joint blind symbol-code) recovery is proposed which allows us to derive a finite set of multiple-antenna schemes for a fixed number of transmit antennas. Identifiability of the proposed tensor model is discussed, and a blind multiuser detection receiver based on the alternating least squares algorithm is considered for performance evaluation of several multiple-antenna CDMA schemes derived from the constrained modeling approach.