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Code-division multiple-access (CDMA) schemes based on block spreading implement the spreading of entire data blocks rather than single symbols, thus achieving a higher robustness against the frequency selectivity of the channel and allowing the use of efficient modulation/equalization schemes operating in the frequency domain (FD). In this paper, we present a new block CDMA (B-CDMA) system where a single cyclic prefix (CP) is used at the end of each spread block. This provides a higher spectral efficiency with respect to existing schemes. By observing that complete orthogonality among users is achievable only for half-loaded systems on dispersive channels, we introduce new criteria for the design of spreading and despreading sequences, which aim at minimizing the mean-square error at the output of the despreader. For the equalization of the received signal, we propose an iterative block decision feedback equalizer, which iterates between equalization and decoding. Equalization filters are designed to minimize the mean-square error and take into account the residual interference due to the nonorthogonality of the spreading sequences. The performance of B-CDMA is evaluated in an uplink wireless scenario and compared to existing CDMA schemes.