Multicarrier code division multiple access (MC-CDMA) systems are well suited for high data rate wireless multimedia services, due to their ability to convert frequency-selective fading channels to distinct flat fading channels with low complexity fast Fourier transform (FFT) devices. However, when multiple users are present, the performance of MC-CDMA systems is degraded by the multiuser interference (MUI) when the channel is frequency-selective. In order to mitigate MUI, we present a joint algorithm that combines transmit power control, antenna array processing and multiuser detection at the receiver. Interestingly, the frequency-selectivity that entails the MUI also provides multipath diversity which can help suppress the MUI. Performance of the algorithm in a number of MC-CDMA system models is evaluated in terms of the average transmit power to achieve the target signal to interference plus noise ratio (SINR). Simulations confirm the outstanding performance of this algorithm compared with the existing ones in MC-CDMA systems.