An OFDM transmitter spreads original data symbols with a complex-valued spreading matrix derived from a discrete Fourier transform. Spread data symbols are mapped to OFDM subcarriers. Spreading and mapping are configured to produce a transmitted spread-OFDM signal with a low peak-to-average power ratio (PAPR) and orthogonal code spaces. In MIMO systems, the complex-valued spreading matrix can comprise a MIMO precoding matrix, and the code spaces can comprise MIMO subspaces. In Cooperative-MIMO, a combination of low code-space cross correlation and low PAPR can be achieved.