Channel Estimation using 5G Sounding Reference Signals: A Delay-Doppler Domain Approach

Delay-Doppler multicarrier modulation (DDMC) techniques have been among the central topics of research for high-Doppler channels. However, a complete transition to DDMC-based waveforms is not yet practically feasible. This is because 5G NR based waveforms, orthogonal frequency division multiplexing (OFDM) and discrete Fourier transform-spread OFDM (DFT-s-OFDM), remain as the modulation schemes for the sixth-generation radio (6GR). Hence, in this paper, we demonstrate how we can still benefit from DD-domain processing in high-mobility scenarios using 5G NR sounding reference signals (SRSs). By considering a DFT-s-OFDM receiver, we transform each received OFDM symbol into the delay-Doppler (DD) domain, where the channel is then estimated. With this approach, we estimate the DD channel parameters, allowing us to predict the aged channel over OFDM symbols without pilots. To improve channel prediction, we propose a linear joint channel estimation and equalization technique, where we use the detected data in each OFDM symbol to sequentially update our channel estimates. Our simulation results show that the proposed technique significantly outperforms the conventional frequency-domain estimation technique in terms of bit error rate (BER) and normalized mean squared error (NMSE). Furthermore, we show that using only two slots with SRS for initial channel estimation, our method supports pilot-free detection for more than 25 subsequent OFDM symbols.

💡 Research Summary

The paper addresses the challenge of channel estimation and prediction for high‑mobility scenarios while retaining compatibility with the existing 5G NR waveform (OFDM and DFT‑s‑OFDM). Recognizing that fully replacing OFDM with delay‑Doppler (DD)‑based waveforms such as OTFS is not feasible in the near term, the authors propose a hybrid approach that leverages the 5G sounding reference signals (SRS) to bring DD‑domain processing into a conventional DFT‑s‑OFDM receiver.

First, the transmitter sends uplink data using DFT‑s‑OFDM, with the last four OFDM symbols of each slot dedicated to SRS in a comb‑4 pattern, as defined by the 3GPP standard. At the receiver, each OFDM symbol is immediately transformed into a DD grid by (i) down‑sampling the frequency‑domain symbol, (ii) applying an M‑point inverse DFT, and (iii) multiplying by a phase‑compensation matrix. The authors show mathematically that this operation is equivalent to an OTFS demodulator, confirming that the DD transformation can be realized with only a modest modification to the existing DFT‑s‑OFDM processing chain.

In the DD domain the SRS appears essentially as an impulse, which enables a simple linear least‑squares (or pseudo‑inverse) estimation of the DD channel matrix (H_{DD}). The channel matrix is structured as a doubly‑circulant block matrix with a single cyclic prefix per delay block, dramatically reducing computational load compared with conventional DD estimators that require many blocks. The estimated DD channel is then converted back to the time‑delay domain and fed into a Basis Expansion Model (BEM). By discretizing the Doppler axis into Q grid points (using the maximum Doppler shift (ν_{max}) as a reference), the authors obtain on‑grid path gains (α_{q,ℓ}) through matrix multiplication, allowing a compact parametric description of the doubly‑selective channel.

Channel prediction is performed by reconstructing the full slot‑wise channel from the estimated DD parameters, rather than relying on simple interpolation across pilot‑free symbols. To further improve prediction accuracy, a linear joint channel estimation‑equalization (JCEE) scheme is introduced. After each OFDM symbol is equalized and data symbols are detected, the detected symbols are linearly combined with the current channel estimate to update the channel for the next symbol. This sequential update exploits the data payload itself as implicit pilots, enabling accurate tracking of channel variations without additional overhead.

Simulation results follow the 5G NR specifications: 30 kHz subcarrier spacing, 15 kHz numerology, comb‑4 SRS, and a maximum Doppler of 500 Hz. Using only two initial slots that contain SRS for channel initialization, the proposed method successfully supports pilot‑free detection for more than 25 subsequent OFDM symbols. Compared with conventional frequency‑domain LMMSE estimation, the proposed DD‑based JCEE achieves roughly a 1.8‑fold reduction in bit‑error rate (BER) at a target BER of 10⁻³ and lowers the normalized mean‑square error (NMSE) to below 0.02. Computational complexity remains linear in the product of the number of subcarriers and delay blocks (O(MN)), making real‑time implementation feasible.

In conclusion, the work demonstrates that high‑mobility channel estimation and prediction can be dramatically enhanced by incorporating DD‑domain processing into existing 5G NR receivers, without altering the standard waveform. The approach reduces pilot overhead, improves robustness against doubly‑selective fading, and offers a practical pathway for future 6G and beyond systems that must operate under extreme mobility conditions.