Transitioning from Deterministic Transforms to Neural Approximations in OTFS

Tajinder Singh

Assistant Professor

Department of Mathematics

Government college, Hoshiarpur

Email: tajindersi786@gmail.com

Abstract:

Orthogonal Time-Frequency Space (OTFS) modulation relies on a cascade of deterministic unitary operators, most notably the Inverse Symplectic Finite Fourier Transform and the Inverse Fast Fourier Transform (IFFT), to map delay-Doppler symbols into a time-domain waveform suitable for doubly-selective channels[1]. While the algebraic exactness of these transforms yields tight bounds on estimator variance and preserves orthogonality up to machine precision, the  complexity of the IFFT and the  cost of the joint delay-Doppler operation become non-trivial as frame sizes scale toward massive MIMO regimes. This work develops a theoretical synthesis describing the substitution of these exact operators by parametric Deep Neural Network (DNN) approximations , whose forward pass executes in fixed depth at the cost of a controlled bias term. We formalize the resulting tradeoff via a decomposition of the Mean-Squared Error (MSE) into approximation, estimation, and quantization components, and we derive sufficient conditions under which the neural surrogate retains a Signal-to-Noise Ratio (SNR) penalty bounded by  in network width [2]. The analysis suggests that latency reductions are achievable without catastrophic loss of orthogonality, provided spectral regularization is enforced on the learned weights.

Keywords: OTFS modulation, IFFT approximation, deep unfolded networks, delay-Doppler estimation, MSE bounds.