, which operates in a frequency selective fading channel. The zero forcing (ZF) technique is applied to accomplish multi user detection (MUD). A Lagrange multiplier method is applied to obtain a one-step solution for optimal power and bit allocations in this system. The resulting algorithm is advantageous over an alternative Greedy algorithm, because it does not require a timeconsuming iterative procedure for its implementation. The algorithm assigns bits and power for all users according to the channel state information (CSI), which is assumed to be fully or partially available to the transmitter. The simulation results show the proposed algorithm operates successfully in multiple user access scenarios.