UW-OTFS: Unique Word OTFS

• UW-OTFS is a modulation scheme that replaces conventional pilot signals with time-domain unique word sequences to enable robust channel estimation in doubly-dispersive environments.
• It leverages Zadoff–Chu and other CAZAC sequences to achieve leakage-free estimation, higher spectral efficiency, and simplified processing in both SISO and MIMO setups.
• Implementation benefits include improved BER and NMSE performance under high mobility, efficient LMMSE estimation, and effective MIMO processing through cyclic-delay diversity.

UW-OTFS (Unique Word Orthogonal Time Frequency Space) refers to a family of physical-layer transmission and channel estimation schemes within the OTFS modulation framework that replace conventional pilot and guard structures with time-domain unique word sequences, typically leveraging Zadoff–Chu (ZC) or other constant amplitude, zero autocorrelation (CAZAC) sequences. UW-OTFS aims to achieve efficient, robust, and low-complexity channel estimation, particularly under highly dispersive or oversampled channel conditions, and in both SISO and MIMO settings. It offers substantial improvements in spectral efficiency, estimation accuracy, and implementation practicality relative to embedded delay–Doppler (DD) impulse pilots or scattered pilot paradigms (Bomfin et al., 2021, Zedka et al., 14 Jan 2026).

1. OTFS and the Challenge of Channel Estimation

OTFS modulation maps information symbols onto a two-dimensional delay–Doppler (DD) grid before transformation into the time–frequency (TF) domain for transmission. This approach significantly enhances resilience to doubly-dispersive (time- and frequency-selective) channels by spreading symbols over both time and frequency. The canonical OTFS transmit signal on the DD grid is:

$$s(t) = \sum_{\tau,\nu} X(\tau,\nu)\, e^{j2\pi\nu(t-\tau)}\, \text{rect}\left(\frac{t-\tau}{T}\right)$$

Channel estimation in practical OTFS implementations, especially in oversampled, pulse-shaped, and fractional-delay scenarios, is complicated by data-to-pilot leakage, spectral inefficiency of DD-pilot guards, and the non-localized energy distribution after fractional timing offsets or Doppler shifts. These effects are exacerbated in high-mobility and MIMO environments (Bomfin et al., 2021, Zedka et al., 14 Jan 2026).

2. UW-OTFS Frame Design and Transmitter Structure

In UW-OTFS, the frame incorporates unique word pilots placed in oversampled time-domain zero-guard intervals, replacing traditional DD impulse pilots or large guard regions. For SISO and MIMO, the frame structure can be generalized as follows:

• Frame Composition: Each transmit antenna emits a frame with two bracketing unique word (UW) blocks—preface and postface—separated by data sub-blocks, each protected with a cyclic prefix (CP). Every UW is a cyclically shifted and power-normalized ZC sequence to enable collision-free, multi-antenna estimation.
• UW Insertion via CDD (MIMO): Cyclic-delay diversity (CDD) achieves spatial distinguishability by circularly shifting UWs and data sub-blocks per-antenna by $n_t(N_{UW}/N_t)$. The resulting frame for transmit antenna $n_t$ is:

$$x_\text{frame}^{(n_t)} = [\, \widetilde{x_{UW,\text{preface}}^{(n_t)}}\, |\, \widetilde{x_0^{(n_t)}}\, |\; ...\; |\, \widetilde{x_{M-1}^{(n_t)}}\, |\, \widetilde{x_{UW,\text{postface}}^{(n_t)}}\, ]$$

where $\widetilde{}$ denotes CP insertion and $M$ the number of sub-blocks.

In oversampled, pulse-shaped OTFS with UW-OTFS ("UW-OFDM precoded" approach), construction employs a non-systematic precoder $G$, zero-pads (matrix $B$) to the oversampled size $M'$, and applies an $M'$-point IDFT, yielding:

$S_d = \alpha_d F_{M'}^H B G X$

with $S_d$ partitioned into an "upper" data part and a lower zero guard interval (GI), into which the time-domain UW pilot is directly embedded (Zedka et al., 14 Jan 2026).

3. Channel Estimation Methodologies in UW-OTFS

Channel estimation exploits the non-interfering, leakage-free nature of time-domain UWs:

Frequency-Domain LS Estimation (Classical OTFS)

1. UW Observation: After CP removal and DFT, the received UWs at each receive antenna are:

$$Y_{UW,u}^{(n_r)} = ( \bar \Lambda_u^{(n_r)} + \tilde \Lambda_{e,u}^{(n_r)} ) X_{UW} + W_{UW,u}^{(n_r)}$$

2. Elementwise LS: Estimate channel frequency response by elementwise division:

$\hat \Lambda_u^{\,'(n_r)} = Y_{UW,u}^{(n_r)} / X_{UW}$

3. Antenna Separation: Applying IDFT and CDD-based slicing yields per-antenna channel estimates.

Time-Domain LMMSE in Oversampled/Pulse-Shaped UW-OTFS

1. Time-Domain Pilot: UW (flat-spectrum or shaped) is transmitted in the guard interval.
2. Observations: After the channel and AWGN, the last $M_h$ samples of each block are collected:

$$Y_{ce}[m,n] = r_u[m + M'n + k_h],\quad m = 0, ..., M_h-1,\ n = 0, ..., N-1$$

1. Linear System: Model as $y_{ce} = A_{ce} h_{ce} + w_{ce}$, where $A_{ce}$ is known and full-rank, and $h_{ce}$ comprises the $M_h N$ channel parameters.
2. LMMSE Solution:

$$\hat h_{ce} = \Omega_{ce} y_{ce},\quad \Omega_{ce} = A_{ce}^H (A_{ce}A_{ce}^H + \gamma I)^{-1}$$

with $A_{ce}$ eigendecomposed offline for computational efficiency (Zedka et al., 14 Jan 2026).

This methodology eliminates pilot/data overlap and leakage, providing unbiased estimates even under severe fractional delay or Doppler.

4. Frame Optimization and Trade-offs

Frame optimization in UW-OTFS aims to balance the estimation error, Doppler-induced ICI, and spectral efficiency:

• Selection of $M$ (number of sub-blocks): Increasing $M$ improves Doppler coherence (reducing Doppler error $\sigma_{DE}$) but places data blocks farther from the UWs, raising channel estimation error ($\sigma_{CE}$). The total error for subcarrier $k$ in block $m$ is:

$$\sigma_{tot,m,k}^2 = \sigma_{CE,m,k}^2 + \sigma_{DE,m,k}^2$$

Optimal $M^*$ minimizes $\sum_{m,k} (\sigma_{CE,m,k}^2 + \sigma_{DE,m,k}^2)$ for fixed grid size (Bomfin et al., 2021).

• Spectral Efficiency: UW-OTFS without extensive DD guards delivers a 36% higher spectral efficiency compared to embedded-pilot CP-OTFS. For example, with $M=32$, $N=16$, $M'=128$, $M_g=9$, $M_{cp}=8$, $M_s^{(A)}=49$, $M_s^{(B)}=44$, the respective spectral efficiencies are $\eta_A\approx2.612$ bit/s/Hz and $\eta_B^*\approx1.968$ bit/s/Hz (Zedka et al., 14 Jan 2026).

5. MIMO UW-OTFS: Diversity and Combining

UW-OTFS naturally extends to MIMO through:

• Cyclic-Delay Diversity (CDD): CDD shifts (by $n_t(N_{UW}/N_t)$) make the multi-antenna convolution separable, such that each antenna’s channel may be estimated independently and efficiently from the same UW sequence.
• Effective SISO Channel: After processing, the convolved MIMO channel reduces to a bank of equivalent single-antenna channels.
• Maximal-Ratio Combining (MRC): FD observations are combined per sub-block:

$$Y_{eq,m} = \frac{\sum_{n_r}\hat\Lambda_m^{(n_r)} Y_m^{(n_r)}}{\left(\sum_{n_r} \hat\Lambda_m^{(n_r)\dagger}\hat\Lambda_m^{(n_r)}\right)^{1/2}}$$

After MRC, detection proceeds as in the SISO case (Bomfin et al., 2021).

6. Comparative Performance Results and Implementation Considerations

Comprehensive empirical evaluations demonstrate:

• BER and NMSE: UW-OTFS avoids the error floor of embedded-pilot OTFS under both pedestrian (200 km/h) and high-mobility (400 km/h) conditions; its NMSE decays steadily with increasing $E_b/N_0$ due to leakage immunity.
• Out-of-band (OOB) Emissions: Shaped UWs yield PSD as low as traditional UW-OFDM, while Dirac pilots substantially increase OOB.
• Spectral Benefits: No large DD guard, and leakage-free estimation permit a $\approx$36% spectral-efficiency gain.
• PAPR: The increase in PAPR is moderate ($\approx1.1$ dB over CP-OTFS, despite the extra pilot energy).
• Complexity: Dominant costs are small FFTs (or IDFTs), LS/LMMSE estimation, and—if MIMO—MRC and simple interpolation. Offline eigendecomposition of system matrices further minimizes online computational burdens (Bomfin et al., 2021, Zedka et al., 14 Jan 2026).

Aspect	Conventional Embedded-Pilot OTFS	UW-OTFS
Channel Estimation	DD domain, suffers leakage	Leakage-free, time-domain UW
Spectral Efficiency	Lower (large DD guards needed)	36% higher (no DD guard)
BER/FER	Error floor, esp. with oversampling	No floor under same conditions
MIMO Support	Needs orthogonal pilots or antenna partition	Handled via CDD, no extra pilots
Out-of-band Emissions	Potentially high	As low as UW-OFDM with shaping

7. Key Advantages and Distinctions

UW-OTFS offers several structural and operational advantages over embedded-pilot and scattered pilot OTFS schemes:

• Leakage-Free Estimation: Time-domain UWs, placed outside the data region, render channel estimation immune to fractional delay/Doppler-induced spreading.
• Spectral Efficiency: Large DD guards are obviated, and all available DD grid points can be used for data.
• Efficient MIMO Operation: CDD at the transmit end allows for pilot sharing without mutual interference; simple receiver-side processing (MRC) yields an effective SISO model.
• Low Complexity: Channel estimation and per-block LMMSE detection do not require large-matrix inversion in the DD domain; system matrices related to pilot structures can be precomputed offline.
• Implementation Flexibility: The UW-in-frame approach unifies pilot design and transmit diversity, facilitating rapid adaptation to varying channel and mobility regimes (Bomfin et al., 2021, Zedka et al., 14 Jan 2026).

A plausible implication is that future wireless systems operating in high-Doppler, high-mobility, and oversampled settings may systematically prefer UW-based OTFS to approaches that rely on embedded DD pilots, both for performance and practical complexity reasons.