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This paper presents noise suppression linearly constrained least square constant modulus algorithm (LSCMA) for blind suppression of multiuser interferences cancellation in CDMA system. The conventional least square constant modulus algorithm (LSCMA) is difficult to converge to the desired user in the system that has several constant modulus signals. To overcome this shortage, a linearly constrained LSCMA algorithm is proposed by applying the linear constrained condition to the LSCMA. To further enhance the performance, we make orthonormalize the weight vector and the noise subspace, and use the noise subspace to impose multiple constraints on the cost function of LSCMA. The Lagrange method and the partial Taylor-series expansion are combined to update the weight vector. In addition, the stational points and output SINR performance are analyzed in theory. The simulation results demonstrate that the proposed algorithm has superior performance and is more robust in the case of random initial value.