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A block-spreading code division multiple access (BS-CDMA) system is proposed for broadband uplink transmission, giving rise to a significantly improved multiuser performance without using complex multiuser detection techniques. This is because the code orthogonality is easily maintained when channel variation across the consecutive blocks, in a block-by-block high-speed transmission, is negligible. The proposed system uses frequency domain equalisation at the receiver to combat multipath interference efficiently over frequency selective fading channels. We propose despreading before equalisation, which reduces the frequency domain process to symbol-wise operation. A cell-specific scrambling code is employed to suppress other-cell interference for uplink transmission in a multicell system. Our analytical and simulation studies show that the proposed BS-CDMA system has superior multiuser performance over the conventional direct sequence CDMA and cyclic prefix CDMA systems for uplink transmission.