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Multiple access interference (MAI) is the main factor affecting the performance of channel estimation techniques for code division multiple access (CDMA) systems. Although, several multi-user channel estimation algorithms have been proposed to mitigate MAI, these algorithms require high computational complexities. In this paper, we address the problem of least squares (LS) mobile channel estimation at high channel efficiency that requires a short training sequence along with the spreading sequences. Then, we employ an efficient iterative method based on conjugate gradient (CG) algorithm to reduce the computational complexity of the estimation method. Computer simulations illustrate that the proposed method performs almost identical to the exact LS estimate for reasonable training lengths.