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In order to exploit the presence of non-zero autocorrelation between consecutive samples of channel variations, predictive schemes based on a recursive least squares (RLS) adaptive algorithm have been proposed. The main motivation for using RLS is its fast convergence property. The RLS algorithm places enormous computational burden on the transmit power control system. In slow power control, however, the fast convergence property is not a stringent requirement. Therefore, we propose a predictive power control scheme based on a least-mean-square (LMS) algorithm. Unlike the RLS algorithm, the LMS algorithm is simple to implement and has low computational complexity. Furthermore, the LMS algorithm has better tracking properties than the RLS algorithm in a nonstationary environment. We demonstrate, through simulation, that a performance gain of up to 0.5 dB in terms of the standard deviation of transmit power control error, over the conventional closed-loop transmit power control, can be achieved through the use of the LMS algorithm. Furthermore, we optimise the performance of the closed-loop power control based on parameters of the LMS predictor, namely adaptation constant and predictor order.