Interleave Frequency Division Multiplexing

In this letter, we study interleave frequency division multiplexing (IFDM) for multicarrier modulation in static multipath and mobile time-varying channels, which outperforms orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), and affine frequency division multiplexing (AFDM) by considering practical advanced detectors. The fundamental principle underlying existing modulation techniques is to establish sparse equivalent channel matrices in order to facilitate the design of low-complexity detection algorithms for signal recovery, making a trade-off between performance and implementation complexity. In contrast, the proposed IFDM establishes an equivalent fully dense and right-unitarily invariant channel matrix with the goal of achieving channel capacity, ensuring that the signals undergo sufficient statistical channel fading. Meanwhile, a low-complexity and replica maximum a posteriori (MAP)-optimal cross-domain memory approximate message passing (CD-MAMP) detector is proposed for IFDM by exploiting the sparsity of the time-domain channel and the unitary invariance in interleave-frequency-domain channel. Numerical results show that IFDM with extremely low-complexity CD-MAMP outperforms OFDM, OTFS, and AFDM with state-of-the-art orthogonal approximate message passing detectors, particularly at low velocities.