Low-Complexity Pilot-Aided Doppler Ambiguity Estimation for OTFS Parametric Channel Estimation

Orthogonal Time Frequency Space (OTFS) modulation offers robust performance in high-mobility scenarios by transforming time-varying channels into the delay-Doppler (DD) domain. However, in high-mobility environment such as emerging 5G Non-Terrestrial Networks (NTN), the extreme orbital velocities of Low Earth Orbit (LEO) satellites frequently cause the physical Doppler shifts to exceed the fundamental grid range. This Doppler ambiguity induces severe model mismatch and renders traditional MLE channel estimators ineffective. To address this challenge, this paper proposes a novel low-complexity pilot-aided Doppler ambiguity detection and compensation framework. We first mathematically derive the OTFS input-output relationship in the presence of aliasing, revealing that Doppler ambiguity manifests itself as a distinct phase rotation along the delay dimension. Leveraging this insight, we developed a two-stage estimator that utilizes pairwise phase differences between pilot symbols to identify the integer ambiguity, followed by a refined Maximum Likelihood Estimation (MLE) for channel recovery. We investigate two pilot arrangements, Embedded Pilot with Guard Zone (EP-GZ) and Data-Surrounded Pilot (DSP), to analyze the trade-off between interference suppression and spectral efficiency. Simulation results demonstrate that the proposed scheme effectively eliminates the error floor caused by ambiguity, achieving Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) performance comparable to the exhaustive search benchmark while maintaining a computational complexity similar to standard MLE.

💡 Research Summary

The paper addresses a critical challenge for Orthogonal Time Frequency Space (OTFS) modulation in high‑mobility scenarios such as 5G Non‑Terrestrial Networks (NTN) that employ Low‑Earth‑Orbit (LEO) satellites. In these environments the physical Doppler shift can exceed the fundamental Doppler grid range (‑N/2 … N/2), causing a “Doppler ambiguity” where the true normalized Doppler index kᵢ wraps around the grid by an integer multiple Nₐₘb,i. The authors first derive the OTFS input‑output relationship under this aliasing condition and show that while the slow‑time (Doppler) matrices remain periodic and thus hide the ambiguity, the fast‑time (delay) phase‑rotation matrix D(kᵢ) acquires an additional deterministic phase term Φ(Nₐₘb,i) that varies linearly with the delay index. This phase term creates a severe model mismatch for conventional parametric channel estimators, especially Modified Maximum Likelihood Estimation (MLE), which assume Nₐₘb,i = 0.

To resolve the ambiguity without resorting to exhaustive search (Extended MLE), the authors propose a low‑complexity, pilot‑aided two‑stage estimator. In the first stage, non‑coherent energy accumulation is used to locate pilot symbols in the delay‑Doppler (DD) grid. In the second stage, the integer ambiguity Nₐₘb,i is estimated by exploiting pairwise phase differences between pilots that belong to the same propagation path. The phase difference between two pilots separated by Δl delay bins equals 2π Nₐₘb,i Δl / M, allowing Nₐₘb,i to be recovered via simple integer rounding after averaging over multiple pilot pairs, which provides robustness against noise.

Once Nₐₘb,i is known, the received signal is compensated by multiplying with the inverse of Φ(Nₐₘb,i), thereby removing the spurious fast‑time rotation. A refined MLE is then applied to estimate the fractional Doppler component κᵢ and the complex path gain hᵢ. The process is repeated with successive interference cancellation (SIC) to detect weaker paths.

Two pilot placement strategies are examined: (1) Embedded Pilot with Guard Zone (EP‑GZ), where zero‑guard regions surround each pilot to suppress inter‑symbol interference (ISI) caused by channel spreading, and (2) Data‑Surrounded Pilot (DSP), which eliminates guard zones to maximize spectral efficiency at the cost of increased pilot‑data interference. Both configurations are shown to enable accurate ambiguity detection; EP‑GZ offers higher estimation reliability, while DSP provides better bandwidth utilization.

Simulation results, based on S‑band (2 GHz) LEO scenarios with sub‑carrier spacings of 15, 30, and 60 kHz, demonstrate that the proposed method eliminates the error floor observed with conventional MLE. Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) curves closely match those of the exhaustive‑search benchmark and the ideal perfect‑CSI case, while the computational complexity remains comparable to standard MLE (linear in the number of pilots and paths) rather than exponential.

In summary, the paper delivers a mathematically grounded, practically feasible solution for Doppler‑ambiguous OTFS channel estimation in NTN. By converting the ambiguity into a measurable phase rotation and resolving it with simple pilot‑based phase‑difference processing, the authors achieve near‑optimal performance with low complexity, paving the way for reliable OTFS deployment in future satellite‑aided 5G/6G networks.