Instantaneous Polarimetry with Zak-OTFS

TL;DR

The paper tackles the challenge of instantaneous polarimetry by enabling full $2\times 2$ polarimetric channel estimation within a single transmission frame. It introduces Zak-OTFS with a pulsone in the delay-Doppler domain and a GDAFT-derived spread waveform that are mutually unbiased, allowing the receiver to recover all four polarimetric components with near-linear complexity in the time-bandwidth product $BT$. The proposed crystallization-based design and cross-ambiguity processing yield ideal target detection and accurate delay/Doppler estimation, with improved clutter resilience over phase-coded and FMCW methods. The results indicate substantial reductions in latency and computational burden, enabling real-time polarimetric sensing in ISAC systems and motivating further experimental validation.

Abstract

Polarimetry, which is the ability to measure the scattering response of the environment across orthogonal polarizations, is fundamental to enhancing wireless communication and radar system performance. In this paper, we utilize the Zak-OTFS modulation to enable instantaneous polarimetry within a single transmission frame. We transmit a Zak-OTFS carrier waveform and a spread carrier waveform mutually unbiased to it simultaneously over orthogonal polarizations. The mutual unbiasedness of the two waveforms enables the receiver to estimate the full polarimetric response of the scattering environment from a single received frame. Unlike existing methods for instantaneous polarimetry with computational complexity quadratic in the time-bandwidth product, the proposed method enables instantaneous polarimetry at near-linear complexity in the time-bandwidth product. Via numerical simulations, we show ideal polarimetric target detection and parameter estimation results with the proposed method, with improvements in computational complexity and greater clutter resilience over comparable baselines.

Figures (5)

• Figure 1: Comparison of different approaches for polarimetry. (a) Sequential polarimetry with FMCW transmits polarized FMCW waveforms over two frames, with each frame subdivided into two halves with an up-chirp and a down-chirp respectively. The associated Doppler resolution is $2/T$ and the computational complexity is $\mathcal{O}(B^2T^2)$. (b) Instantaneous polarimetry with Zak-OTFS transmits a Zak-OTFS pulsone and a mutually unbiased spread waveform obtained via a unitary transformation of the pulsone in a single frame. Compared to the sequential approach in (a), the proposed approach has $2 \times$ smaller latency, $2 \times$ improved Doppler resolution of $1/T$, and a computational complexity of only $\mathcal{O}(BT \log T)$.
• Figure 2: Heatmaps of estimated channels for a four-target environment with two targets with equal $h^{(p)}_{\mathsf{HH}} = 0.7$ & $h^{(p)}_{\mathsf{HV}} = h^{(p)}_{\mathsf{VH}} = h^{(p)}_{\mathsf{VV}} = 0$, and two targets with unequal $h^{(p)}_{\mathsf{HV}} = h^{(p)}_{\mathsf{VH}} \in \{0.3,0.95\}$ & $h^{(p)}_{\mathsf{HH}} = h^{(p)}_{\mathsf{VV}} = 0$. (a) & (d): Sequential polarimetry via FMCW detects two false targets ("ghost targets") in addition to the two true targets in the $\mathsf{HH}$ channel, and fails to detect the lower energy target in the $\mathsf{VH}$ channel due to the high sidelobes of the waveform. (b)-(c) & (e)-(f): Instantaneous polarimetry via mutually unbiased phase-coded and Zak-OTFS waveforms detects all four targets correctly in the $\mathsf{HH}$ and $\mathsf{VH}$ channels.
• Figure 3: Histograms for single polarimetric target detection under the target present and target absent hypotheses. (a)-(c): Uni-polarization is insufficient for detecting polarimetric targets. (d): Dual-polarized FMCW is not optimal for polarimetric target detection due to high waveform sidelobes & false target detections (cf. Figs. \ref{['fig:heatmaps']}(\ref{['fig:heatmaps_11f']}) & \ref{['fig:heatmaps']}(\ref{['fig:heatmaps_21f']})). (e)-(f): Dual-polarized phase-coded and Zak-OTFS waveforms are optimal for polarimetric target detection (cf. Figs. \ref{['fig:heatmaps']}(\ref{['fig:heatmaps_11p']})-(\ref{['fig:heatmaps_11z']}) & \ref{['fig:heatmaps']}(\ref{['fig:heatmaps_21p']})-(\ref{['fig:heatmaps_21z']})).
• Figure 4: Single target detection and estimation performance. (a): Receiver operating characteristic (ROC) curve showing ideal target detection with dual-polarized Zak-OTFS and phase-coded waveforms. The performance degrades with FMCW and/or uni-polarized waveforms. (b)-(c): Root mean squared error (RMSE) for delay and Doppler estimation, normalized by the corresponding delay and Doppler resolutions of $1/B$ and $1/T$. (b): Delay RMSE is similar for dual-polarized Zak-OTFS, phase-coded and FMCW systems at high signal-to-noise ratio (SNR), with significant improvements over uni-polarized waveforms. (c): Doppler RMSE is similar for dual-polarized Zak-OTFS and phase-coded waveforms at high SNR, with $\sim 1.5 \times$ improvement over FMCW due to no loss in Doppler resolution. Significant improvements with dual-polarized vs uni-polarized waveforms.
• Figure 5: Instantaneous polarimetry via Zak-OTFS exhibits greater resilience to clutter as compared to competing methods.

Theorems & Definitions (2)

• Definition 1: EURASIP2025Mehrotra2025_WCLSpread
• Theorem 1: EURASIP2025Mehrotra2025_WCLSpread