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The blind beamforming based on the maximum signal-to-(interference plus noise) ratio (MSINR) algorithm can recover a desired user signal among several cochannel users without using a reference signal and without assuming prior knowledge of the array direction characteristics, The main drawback of MSINR algorithm is sensitivity to carrier frequency offsets (CFO). The CFO will cause the continuous phase rotate along with processing time and collapses the original signal constellation, especially in high QAM modulation. Hence, the effect of CFBC will induce high bit error rate and degrade the receiver performance. In this paper, we propose a new smart antenna array to mitigate multiple access interference and compensate the carrier frequency offset. The smart antenna arrays utilize blind adaptive beamforming, which is based on MSINR algorithm and the multimodulus algorithm (MMA). The MSINR algorithm is combined with the (MMA) and the algorithm is called MSINR-MMA. The motivation behind combining MMA adaptation with MSINR adaptation is to combine the best features of each algorithm to gain a more robust adaptation criterion. The MSINR- MMA doesn't require explicit direction of arrival estimation or training signals derived for the Ds- CDMA system and is shown to reduce interferences from other users significantly, thus increases the system's user capacity and compensates the carrier frequency offset.