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A low complex interference cancellation via modified suboptimum search algorithm in conjunction with a primary stage of reduced rank linear (RRL) multiuser detector for the mobile uplink is proposed. Initial stage is improved through mathematical analysis via Gershgorin algorithm in linear algebra and RRLG detector is introduced. The complexity of the initial stage is evaluated and compared to the recently reported low-complex Fourier interference cancellation method. Depending on the value of the spreading factor of the active users in system, RRLG outperforms the Fourier algorithm, in terms of complexity. The structure of the RRLG method and the suboptimum search algorithm are well suited together and makes them collaboratively work without encountering a high level of complexity. Considering the power profile of the users in the suboptimum search algorithm leaded to even less complexity, yet keeping the performance almost the same. The performance of the structure is obtained via simulations and has been compared to partial parallel interference cancellation (PPIC) method. A good improvement in performance in the low SNR regions, which is difficult to achieve by conventional multiuser detectors and also important as the actual systems are likely to operate in these regions, has been achieved. All the techniques and their modifications introduced in this work consider the complexity as an important issue that enables them suitable for industry and implementation purposes. Another important feature is that the techniques perform on canonical matrix formulations of the system so they can be applied to MC-CDMA and MIMO systems, as well.