OTFS Neural Receiver

Unlike classical receivers that perform channel estimation and symbol detection as separate, sequential modules, the OTFS neural receiver learns to perform both tasks jointly in an end-to-end fashion. A single neural network ingests the received time-domain signal and directly outputs detected symbols, implicitly learning the channel's delay-Doppler response as a latent representation. This eliminates error propagation between decoupled stages and enables the model to learn optimal estimation strategies that are task-aware—the channel is estimated only to the fidelity required for accurate detection, not to an arbitrary metric like Mean Squared Error (MSE). Architectures often employ a convolutional encoder to extract features from the received grid, followed by a recurrent or transformer-based decoder that iteratively refines symbol estimates.

The defining architectural innovation is the direct processing of signals in the delay-Doppler domain rather than the conventional time-frequency domain. In high-mobility scenarios, a time-frequency channel appears rapidly time-varying, requiring complex, frequent re-estimation. By applying an Inverse Symplectic Finite Fourier Transform (ISFFT) at the transmitter and a corresponding SFFT at the receiver, the channel is transformed into a sparse, quasi-static representation in the delay-Doppler domain. The neural receiver exploits this sparsity, using architectures like Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) networks or attention mechanisms that focus computation only on the few non-zero delay-Doppler bins, dramatically reducing the effective degrees of freedom the model must learn.

Classical OFDM receivers fail catastrophically under high Doppler spreads because subcarrier orthogonality is destroyed, causing severe Inter-Carrier Interference (ICI). OTFS modulation, combined with a neural receiver, is inherently resilient. The neural network learns to treat ICI not as unstructured noise, but as a deterministic, learnable transformation in the delay-Doppler domain. By training on diverse channel realizations—including extreme velocities up to 500 km/h and millimeter-wave frequencies—the model internalizes the physics of Doppler-induced dispersion. This enables reliable communication in environments previously considered impossible for broadband wireless, such as high-speed rail, low-earth orbit satellite links, and supersonic aircraft telemetry.

To balance the data hunger of pure black-box neural networks with the sample efficiency of classical algorithms, OTFS neural receivers frequently employ deep unfolding. This methodology takes an iterative optimization algorithm, such as the Message Passing (MP) detector or Approximate Message Passing (AMP) for sparse signal recovery, and unrolls its iterations into a fixed number of neural network layers. Each layer mirrors one algorithm iteration but replaces hand-crafted parameters (like damping factors or shrinkage thresholds) with learnable weights. This injects domain knowledge of the OTFS input-output relation into the architecture, requiring orders of magnitude fewer training samples than a generic deep neural network while still outperforming the classical algorithm by learning optimal parameters from data.

A critical practical concern for real-time receivers is computational complexity. The delay-Doppler channel matrix, while sparse, can be large. OTFS neural receivers address this with sparse attention mechanisms and graph neural networks (GNNs). Instead of computing attention scores across all symbol pairs—a quadratic operation—the model restricts attention to symbol nodes connected by non-zero delay-Doppler taps, which are few. The interference pattern is modeled as a sparse bipartite graph, and a GNN with message passing between variable and factor nodes performs iterative inference. This reduces complexity from O(N²) to O(N) in the number of symbols, enabling implementation on embedded FPGA or ASIC platforms for practical deployment in user equipment.

The most ambitious OTFS neural receivers are trained end-to-end as a single autoencoder, jointly optimizing the transmitter's precoding and the receiver's detection. Crucially, training can be performed without an explicit mathematical channel model. By using a Generative Adversarial Network (GAN) or a diffusion model to learn the distribution of real-world delay-Doppler channel responses from measurement campaigns, the end-to-end system can be trained on this learned channel surrogate. This makes the receiver channel-agnostic—it is optimized for the empirical statistics of real propagation environments, not an idealized model like Jakes' spectrum. The result is a receiver that generalizes robustly to field conditions that violate theoretical assumptions.

The fundamental signal representation space where OTFS modulation operates. Unlike traditional time-frequency grids, the delay-Doppler domain directly represents the physical geometry of the wireless channel—each symbol experiences a specific delay (range) and Doppler shift (velocity). This representation makes the channel sparse, separable, and quasi-static even at high velocities, allowing a neural receiver to learn a compact, interpretable mapping rather than a complex time-varying function.

A core architectural principle of the OTFS neural receiver where a single deep learning model simultaneously performs two traditionally separate tasks:

• Channel Estimation: Learning the delay-Doppler channel response from embedded pilots
• Symbol Detection: Recovering transmitted symbols by inverting the channel effects

This joint optimization eliminates error propagation between cascaded blocks and allows the network to learn task-specific features that a modular pipeline would discard. Architectures typically employ convolutional neural networks or transformers operating on the 2D delay-Doppler grid.

The Inverse Symplectic Finite Fourier Transform (ISFFT) and Symplectic Finite Fourier Transform (SFFT) are the mathematical bridges between the delay-Doppler and time-frequency domains in OTFS. The ISFFT maps QAM symbols from the delay-Doppler grid to the time-frequency plane for OFDM-based transmission, while the SFFT performs the reverse operation at the receiver. A neural receiver can learn to operate directly on the delay-Doppler grid, implicitly learning transformations that outperform these fixed linear transforms under non-ideal conditions like fractional Doppler shifts.

OTFS neural receivers are trained and evaluated on channel models that capture the extreme conditions where traditional OFDM fails:

• Extended Vehicular A (EVA): Models urban multipath at speeds up to 500 km/h
• Tapped Delay Line (TDL): Parameterized models with configurable delay spreads and Doppler profiles
• Ray-tracing based models: Site-specific propagation with precise geometric information
• Clustered Delay Line (CDL): 3GPP standard models capturing spatial consistency

Training across diverse channel distributions is critical for generalization to real-world deployment scenarios.

A classical iterative detection algorithm for OTFS that serves as both a baseline and a structural prior for neural receiver design. Message passing exploits the sparsity of the delay-Doppler channel by passing probabilistic messages between variable nodes (transmitted symbols) and observation nodes (received symbols) on a factor graph. Model-driven neural receivers often unroll these iterations into network layers, replacing hand-crafted damping factors and update rules with learnable parameters, achieving faster convergence and superior bit-error rate performance.

A critical challenge in practical OTFS systems where the Doppler shift is not an integer multiple of the subcarrier spacing, causing inter-Doppler interference (IDI) that spreads energy across multiple Doppler bins. Classical receivers suffer severe performance degradation under fractional Doppler. Neural receivers address this by:

• Learning to deconvolve the smeared Doppler response
• Using attention mechanisms to capture long-range interference patterns
• Incorporating Doppler compensation layers as differentiable components

This capability is essential for operation in realistic high-mobility environments like high-speed rail and low-earth orbit satellite links.