Interleave Frequency Division Multiplexing

TL;DR

This work introduces Interleave Frequency Division Multiplexing (IFDM), a multicarrier scheme that uses a random interleave Π and IF transform U = Π F_N^H to produce a dense, right-unitarily invariant equivalent channel H_eff = F_N Π^{-1} H Π F_N^H, enabling capacity-oriented detection. A low-complexity cross-domain MAMP detector (CD-MAMP) combines a memory-based frontal stage and a nonlinear IF-domain detector to achieve replica MAP-optimal BER with practical complexity, exploiting time-domain sparsity and the unitary invariance of the IF-domain channel. Numerical results demonstrate that IFDM with CD-MAMP outperforms OFDM, OTFS, and AFDM in both static multipath and mobile channels, with gains up to 16 dB in static cases and more than 2 dB at 500 km/h, while achieving substantial runtime reductions (e.g., ~100x faster in 512-subcarrier MIMO scenarios) relative to competing detectors. The approach offers a pathway to high-throughput, robust communication in high-mobility environments by marrying a dense, statistically stable channel model with a highly efficient, replica MAP-optimal detector.

Abstract

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.

Figures (6)

• Figure 1: An IFDM-based multicarrier communication system, where $\bf{\Pi}$ and $\bf{\Pi}^{-1}$ denotes random interleaving and deinterleaving, $\bf{F}^{\mathrm{H}}$ and $\bf{F}$ denote an IFFT matrix and an FFT matrix, respectively, and S/P and P/S denote serial-to-parallel and parallel-to-serial conversion, respectively.
• Figure 2: Comparison of time domain $\bf{H}$ and IF domain ${\bf{H}}_{\mathrm{eff}}$.
• Figure 3: MIMO-IFDM with $N_t$-antenna transmitter and $N_r$-antenna receiver.
• Figure 4: The CD-MAMP detector in IFDM: memory MF detector $\gamma_t(\cdot)$ in the time domain and MMSE nonlinear detector $\phi_t(\cdot)$ in the IF domain.
• Figure 5: Quantile-quantile plot between the estimation signals before and after the inverse IF transform (i.e., $\bf{r}_t$ and $\tilde{\bf{r}}_t$) and ideal Gaussian quantiles with $\mathcal{CN}(\bf{0}, v_{t,t}^{\gamma}\bf{I})$ and $t=1$, where $\bf{s}$ is an equiprobable BPSK signal vector.