Techniques are described for multicarrier multiple access wireless transmission, e.g. orthogonal frequency-division multiple access (OFDMA) transmissions, over frequency selective fading channels. The techniques are designed to maintain constant modulus transmissions for uplink while effectively mitigating intersymbol interference. Specifically, the techniques utilize non-redundant unitary precoding across OFDMA subcarriers to maintain constant modulus transmissions for uplink communications. For example, the techniques involve precoding a block of information symbols and assigning a different subcarrier for each symbol of the block. The subcarriers are selected to be equi-spaced and may be selected, for example, from a phase-shift keying constellation. The number of symbols per block is equal to the number of subcarriers assigned per user. Importantly, even with multiple subcarriers per user, the techniques enable constant modulus transmissions for uplink. Consequently, the techniques may achieve high power and bandwidth efficiency as well as improved performance over conventional OFDMA and GMC-CDMA transmissions.