This thesis study involves designing, implementing and testing of a novel radio resource control algorithm for the closed loop power control in the LTE uplink. Different values of the path loss compensation factor are investigated in the range 0.7-1.0 and an optimal value of 0.8 as allowed by the LTE standard is proposed. Both the ideal and a more realistic case modeled by including delay, error, and power headroom reporting were studied. Simulation results indicated that the closed loop power control with fractional path loss compensation factor is advantageous compared to closed loop power control with full path loss compensation. Using a simple upload traffic model, the closed loop power control with fractional path loss compensation factor improved the system performance in terms of mean bit rate by 68% in the ideal case and 63% in the realistic case. The power headroom report triggering at change in path loss gave better performance than triggering at periodic intervals.