A Hybrid I/O Relation Estimation Scheme for Zak-OTFS Receivers

In this paper, we consider the problem of estimating the delay-Doppler (DD) domain input-output (I/O) relation in Zak-OTFS modulation, which is needed for signal detection. Two approaches, namely, model-dependent and model-free approaches, can be employed for this purpose. The model-dependent approach requires explicit estimation of the physical channel parameters (path delays, Dopplers, and gains) to obtain the I/O relation. Such an explicit estimation is not required in the model-free approach, where the I/O relation can be estimated by reading off the samples in the fundamental DD period of the received pilot frame. Model-free approach has the advantage of acquiring fractional DD channels with simplicity. However, the read-off in the model-free approach provides an estimate of the effective channel only over a limited region in the DD plane but it does not provide an estimate for the region outside, and this can affect the estimation performance depending on the pulse shaping characteristics of the DD pulse shaping filter used. A poorly localized DD pulse shape leads to an increased degradation in performance. Motivated by this, in this article, we propose a novel, yet simple, I/O relation estimation scheme that alleviates the above issue in the model-free approach. We achieve this by obtaining a coarse estimate of the effective channel outside the model-free estimation region using a novel model-dependent scheme and using this estimate along with the model-free estimate to obtain an improved estimate of the overall I/O relation. We devise the proposed estimation scheme for both exclusive and embedded pilot frames. Our simulation results using Vehicular-A, TDL-A and TDL-C channel models with fractional DDs show that the proposed hybrid estimation approach achieves superior performance compared to the pure model-free approach. For example, at a bit error rate (BER) of $1.5 \times 10^{-3}$ , the proposed scheme achieves an SNR gain of about 3.5 dB compared to the model-free approach for sinc filter in Veh-A channel, and this performance gain is achieved with a moderate increase in complexity (e.g., about $2.95\times 10^{8}$ and $8.1\times 10^{8}$ real operations for model-free approach and the proposed scheme, respectively). Also, the proposed scheme performs close to that of the sparse Bayesian learning (SBL) based estimation but at a significantly lesser complexity (e.g., about $8.3\times 10^{12}$ and $8.1\times 10^{8}$ real operations for the SBL based method and the proposed scheme, respectively).