Power control is considered as an important technique to mitigate the near-farfading effect and thus improve the system performance. In this paper, we present an adaptive decentralized power control algorithm. Power control in the uplink direction is been considered The proposed algorithm is a first order algorithm and utilizes bit error rate (BER) as a decision criterion for power update. Pilot bits in the uplink frame are used to measure the BER. We incorporate a nonlinear exponential term in the power update function to improve the speed of convergence of the algorithm which is also demonstrated through simulation results. Changing the adaptation parameter also changes the speed of convergence. The algorithm is examined in a time varying Rayleigh fading environment with frequency selective channel. We also demonstrate that the proposed algorithm achieves gain in the average required signal-to-noise ratio (SNR) value compared to other algorithms. The users are assumed to be mobile during the simulation period The proposed algorithm also performs well at higher mobile speed.