OFDM is widely adopted in modern wireless communication systems, but its power efficiency is limited by high envelope fluctuations. Although various high power-efficiency waveforms have been proposed, most are incompatible with the CP-OFDMA framework and remain ineffective in multi-user downlink transmissions. To address this issue, we propose a constant-envelope (CE) waveform design, which enables low-complexity transceiver architectures while maintaining full compatibility with the prevailing CP-OFDMA framework. Specifically, we start from a general CE FDMA signal model and develop a CP-OFDMA-compatible waveform implementation structure, followed by the design of an optimized CE-constrained pulse-shaping filter to suppress out-of-band emissions. To tackle channel estimation challenge under non-flat frequency-domain pilots induced by CE modulation, we optimize the time-domain binary pilot sequence to achieve frequency-domain CE properties, and then propose a multi-stage method combining delay-domain denoising with power delay profile estimation to facilitate reduced-dimension LMMSE estimation. Subsequently, we design a low-complexity maximum ratio combining-aided LMMSE equalizer by exploiting the periodicity and conjugate symmetry of the CE received signals. To mitigate the downlink peak-to-average power ratio increase caused by FDMA, we further develop a multi-user downlink CE transmission scheme including multiple access mechanism, downlink control information design, and corresponding system-level implementation, which ensures compatibility with the New Radio standard. Numerical results demonstrate that the proposed scheme achieves bit error rate performance close to the ideal case while significantly reducing transceiver complexity compared to existing CE waveform solutions.