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Synchronous code-division multiple-access (CDMA) techniques possess intrinsic protection against co-channel interference when orthogonal codes are used. However, in the presence of multipath propagation, the signals lose their orthogonality property, leading to increased cross correlation. In these cases, channel estimation may be needed in order to improve detection. The former algorithms to estimating the channel response of the CDMA system are used for signal sampled with chip rate. The received signal sampled in chip rate does not satisfy the Nyquist theory and the channel may not be a minimum-phase system that the former algorithms don't work. We propose algorithms for fractionally spaced channel estimation and equalization of a synchronous CDMA system that uses aperiodic spreading code. Simulations have demonstrated the performance of proposed algorithm.