SC-IFDM–FMCW Orthogonal Waveform

• The waveform is a joint construction that combines SC-IFDM data symbols and FMCW chirps using DFT-domain orthogonalization to enable radar-grade sensing and reliable communications.
• It guarantees mutual orthogonality by allocating non-overlapping DFT bins to chirp and data components, effectively eliminating cross-interference and simplifying resource allocation.
• The design supports pilot-free channel estimation and flexible power/resource partitioning, optimizing both sensing SNR and communication throughput in 5G/6G networks.

The SC-IFDM–FMCW orthogonal waveform is a joint waveform for integrated sensing and communication (ISAC) that combines single-carrier interleaved frequency division multiplexing (SC-IFDM) and frequency modulated continuous wave (FMCW) chirps using DFT-domain orthogonalization. This construction enables radar-grade range–Doppler sensing and high-throughput, low-PAPR communication in a single hardware pulse, achieving strictly mutual orthogonality between data and chirp components and eliminating cross-interference. The result is a class of waveforms that unify sensing and data multiplexing within a mathematically rigorous resource grid, with precise resource partitioning and channel estimation properties, making them central to JSAC designs in 5G/6G networks (Boudjelal et al., 16 Mar 2025, Boudjelal et al., 16 Mar 2025, Huang et al., 2 Feb 2026).

1. Technical Construction of SC-IFDM and FMCW Coexistence

Consider $M$ DFT blocks on $N$ subcarriers, forming a two-dimensional DFT-domain grid. SC-IFDM data symbols $X^{\mathrm{SC}}(k,\ell)$ are packed and transformed into time domain via:

$$s^{\mathrm{SC}}[p] = \frac{1}{\sqrt N} \sum_{k=0}^{N-1} X^{\mathrm{SC}}\bigl(k,[p]_M\bigr) e^{j2\pi\frac{k}{MN}p},~~~p=0,\dots,MN-1$$

A discrete-time FMCW chirp is of the form:

$$s^{\mathrm{FMCW}}[p]=\exp\!\left(j\pi \frac{p^2}{MN}\right),\quad p=0,\dots,MN-1$$

Its DFT-domain representation is highly sparse: for each DFT block index $\ell$, only the DFT bin $k = (\ell + M/2) \bmod N$ is nonzero. The composite DFT-domain grid is populated as:

$$X^{\mathrm{comb}}(k,l) = \begin{cases} \sqrt{\psi}\;\omega^l_k\;s^{\mathrm{FMCW}}[l] & [M/2 + l - k]_N = 0 \ X^{\mathrm{SC}}(k, l) & \text{otherwise} \end{cases}$$

where $\psi$ is the chirp-to-data power split and $\omega_k^l=e^{-j2\pi k l/(MN)}$.

The composite time-domain pulse is then constructed by an $MN$-point IDFT. A cyclic prefix (CP) is inserted to manage inter-symbol interference and ensure circular continuity, with the FMCW chirp coefficients shifted appropriately to maintain analog continuity across CP boundaries (Boudjelal et al., 16 Mar 2025, Boudjelal et al., 16 Mar 2025).

2. Orthogonality in the DFT Domain and Mutual Interference Suppression

Orthogonality arises from strict disjoint support of data and chirp elements in the DFT domain:

• The FMCW chirp occupies $$\Omega_{\rm chirp} = \{(k,\ell): k = \ell + M/2 \bmod N\}$$,
• SC-IFDM data symbols use the complementary set $\Omega_{\rm data}$.

This guarantees that

$$\sum_{k=0}^{MN-1} X^{\mathrm{SC}}(k,l) \left(X^{\mathrm{FMCW}}(k,l)\right)^{*}=0$$

for all $l$, and in the time domain,

$\langle s^{\mathrm{SC}}(t), c(t)\rangle = 0$

due to non-overlapping frequency components (Boudjelal et al., 16 Mar 2025, Boudjelal et al., 16 Mar 2025). Any resource trade-off (e.g., between sensing SNR and communication throughput) can be formulated as resource-set partitioning and power allocation within the DFT grid.

3. Enhanced Channel and Sensing Estimation Mechanisms

SC-IFDM–FMCW enables chirp-based, pilot-free channel estimation. At the receiver, the DFT output at “pilot” bins (i.e., chirp support) contains the chirp response and possible data leakage, enabling the following chirp-matched transformation:

$$\widehat Y_1(\beta_1,\alpha_1) = \frac{1}{M} \sum_{l=0}^{M-1} Y_{dp}(k, l) e^{-j\pi\frac{(l-\alpha_1 N-\beta_1)^2}{MN}}$$

where $\alpha_1N+\beta_1$ parameterizes integer delay and Doppler bins. Matching both up-chirp and down-chirp blocks allows unique recovery of per-tap delay, Doppler, and amplitude without dedicated pilot symbols.

This aligns with recent DD-multiplexing generalizations (e.g., ODDM-FMCW, where a ZCA chirp sequence is allocated on complementary DD grid positions, cyclically correlated for delay extraction) and extends naturally to schemes employing square-root Nyquist pulse shaping for ISI control (Huang et al., 2 Feb 2026). The matched filter followed by soft linear detection comprises the front end of both communication and sensing receivers.

4. Resource Partitioning, Spectrum, and PAPR Optimization

The SC-IFDM framework admits precise resource allocation:

• The set $\Omega_{\rm chirp}$ is of size $M$ (one per DFT block), with remaining grid locations supporting arbitrary QAM data.
• The underlying IDFT remains unchanged, permitting transparent integration into existing hardware.

Spectrum shaping is determined by the underlying pulse shape; for instance, using SRRC or similar square-root Nyquist pulses produces low out-of-band emission (OOBE) and tight time–frequency occupancy, closely paralleling advances in ODDM-FMCW waveform design (Huang et al., 2 Feb 2026). By adjusting the power split between chirp and data ($\psi$), one can optimize for desired PAPR and sensing SNR.

The PAPR of the resulting waveform