Effective suppression of multiuser interference (MUI) and mitigation of frequency-selective fading effects within the complexity constraints of the mobile constitute major challenges for broadband cellular downlink transceiver design. Existing wideband direct-sequence (DS) code division multiple access (CDMA) transceivers suppress MUI statistically by restoring the orthogonality among users at the receiver. However, they call for receive diversity and multichannel equalization to improve the fading effects caused by deep channel fades. Relying on redundant block spreading and linear precoding, we design a so-called multicarrier block-spread- (MCBS-)CDMA transceiver that preserves the orthogonality among users and guarantees symbol detection, regardless of the underlying frequency-selective fading channels. These properties allow for deterministic MUI elimination through low-complexity block despreading and enable full diversity gains, irrespective of the system load. Different options to perform equalization and decoding, either jointly or separately, strike the trade-off between performance and complexity. To improve the performance over multi-input multi-output (MIMO) multipath fading channels, our MCBS-CDMA transceiver combines well with space-time block-coding (STBC) techniques, to exploit both multiantenna and multipath diversity gains, irrespective of the system load. Simulation results demonstrate the superior performance of MCBS-CDMA compared to competing alternatives.