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In wireless communication systems with multiple users, the near-far effect and the cochannel interferences decrease the spectral efficiency and system performance. An efficient known method to combat these destructive effects is to properly adjust the transmit powers. A practical and efficient way for power control (PC) in cellular communication systems is the autonomous distributed PC (DPC). In this method, the transmit power of each link is independently modified based on the received signal-to-interference-plus-noise ratio (SINR) reported from the other side of that link. It is known that in a perfect scenario where the reported SINRs are exact, this algorithm converges to the optimum transmit powers. However, in the case of erroneous SINR reports, the transmit powers deviate from their optimum values. This paper addresses the destructive effect of inaccurate SINR reports on the performance of a DPC algorithm. Then, independent variable step-sizes that update the transmit powers are proposed, and convergence of the proposed DPC algorithm to the optimum solution of the original problem is analytically shown. Additionally, a protocol to adaptively tune the step-sizes in our algorithm, which improves the performance of PC in the presence of inaccurate SINR reports, is proposed. Computer simulations are used to study the performance of the proposed method in terms of both the speed of converges and the steady-state accuracy of link qualities.