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This paper details a new orthogonal-frequency-division-multiplexing (OFDM) modulator based on the use of a pseudorandom postfix (PRP)-OFDM and discusses low-complexity equalization and channel estimation/tracking architectures. The main property of this new modulation scheme is the ability to estimate and track the channel variations semi-blindly using order-one statistics of the received signal. Compared with known cyclic prefix OFDM (CP-OFDM) pilot-symbol-assisted modulation (PSAM) schemes, the pilot overhead is avoided: The channel estimation is performed based on the exploitation of pseudorandomly weighted postfix sequences replacing the guard interval contents of CP-OFDM. PRP-OFDM is shown to be of advantage if the target application requires 1) a minimum pilot overhead, 2) low-complexity channel tracking (e.g., high mobility context), and 3) adjustable receiver complexity/performance trade-offs (available due to the similarities of PRP-OFDM to the zero-padded OFDM (ZP-OFDM) modulation scheme) without requiring any feedback loop to the transmitter.