Jointly optimum power and bandwidth allocation for multi-rate FDM and FDMA over overloaded channels

An optimal power and bandwidth allocation problem is considered for multi-rate frequency-division multiplexing (FDM) and frequency-division multiple-access (FDMA) over overloaded channels. We have derived the optimum frequency-division system that minimizes the total transmitted power subject to the QoS of users defined in terms of the transmission rates and the SINR requirements. The necessary and sufficient condition is found for the admissibility of the users, and the optimum power, bandwidth, transmit waveform, and receive waveform are found for each user. It is shown that the optimum frequency-division system performs exactly the same as the optimum CDMA system when all the users have the same transmission rate and channel gain. It is also shown that the optimum frequency-division system always outperforms the ETSC-minimizing code-division system when all the overloading users have the same transmission rate.