Selected mapping (SLM) schemes are commonly employed to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. To decrease the number of inverse fast Fourier transform (IFFT) operations in traditional SLM schemes, the candidate signals can be generated in the time domain by linearly combining the original time-domain transmitted signal with multiple cyclic shift equivalents. However, the weighting coefficients and the number of cyclic shifts should be properly chosen to ensure that the elements of the corresponding frequency domain phase rotation vectors have an equal magnitude. This study presents a number of expressions for meeting this equal-gain-magnitude constraint in orthogonal frequency division multiple access (OFDMA) uplink systems. Of these various solutions, a low-complexity expression is selected to construct the proposed low-complexity scheme that requires only one IFFT. The proposed architecture is proven to be applicable to OFDMA uplink systems using either an interleaved or a sub-band sub-carrier assignment strategy.