Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Das, Arpan, Jesbin, Fathima, Chockalingam, Ananthanarayanan
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:https://arxiv.org/abs/2504.18887
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866915261600235520
author Das, Arpan
Jesbin, Fathima
Chockalingam, Ananthanarayanan
author_facet Das, Arpan
Jesbin, Fathima
Chockalingam, Ananthanarayanan
contents The transceiver operations in the delay-Doppler (DD) domain in Zak-OTFS modulation, including DD domain filtering at the transmitter and receiver, involve twisted convolution operation. The twisted convolution operations give rise to multiple integrals in the end-to-end DD domain input-output (I/O) relation. The I/O relation plays a crucial role in performance evaluation and algorithm development for transceiver implementation. In this paper, we derive discrete DD domain closed-form expressions for the I/O relation and noise covariance in Zak-OTFS. We derive these expressions for sinc and Gaussian pulse shaping DD filters at the transmitter (Tx). On the receiver (Rx) side, three types of DD filters are considered, viz., $(i)$ Rx filter identical to Tx filter (referred to as `identical filtering'), $(ii)$ Rx filter matched to the Tx filter (referred to as `matched filtering'), and $(iii)$ Rx filter matched to both Tx filter and channel response (referred to as `channel matched filtering'). For all the above cases, except for the case of sinc identical filtering, we derive exact I/O relation and noise covariance expressions in closed-form. For the sinc identical filtering case, we derive approximate closed-form expressions which are shown to be accurate. Using the derived closed-form expressions, we evaluate the bit error performance of Zak-OTFS for different Tx/Rx filter configurations. Our results using Vehicular-A (Veh-A) channel model with fractional DDs show that, while matched filtering achieves slightly better or almost same performance as identical filtering, channel matched filtering achieves the best performance among the three.
format Preprint
id arxiv_https___arxiv_org_abs_2504_18887
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Closed-Form Expressions for I/O Relation in Zak-OTFS with Different Delay-Doppler Filters
Das, Arpan
Jesbin, Fathima
Chockalingam, Ananthanarayanan
Information Theory
Signal Processing
The transceiver operations in the delay-Doppler (DD) domain in Zak-OTFS modulation, including DD domain filtering at the transmitter and receiver, involve twisted convolution operation. The twisted convolution operations give rise to multiple integrals in the end-to-end DD domain input-output (I/O) relation. The I/O relation plays a crucial role in performance evaluation and algorithm development for transceiver implementation. In this paper, we derive discrete DD domain closed-form expressions for the I/O relation and noise covariance in Zak-OTFS. We derive these expressions for sinc and Gaussian pulse shaping DD filters at the transmitter (Tx). On the receiver (Rx) side, three types of DD filters are considered, viz., $(i)$ Rx filter identical to Tx filter (referred to as `identical filtering'), $(ii)$ Rx filter matched to the Tx filter (referred to as `matched filtering'), and $(iii)$ Rx filter matched to both Tx filter and channel response (referred to as `channel matched filtering'). For all the above cases, except for the case of sinc identical filtering, we derive exact I/O relation and noise covariance expressions in closed-form. For the sinc identical filtering case, we derive approximate closed-form expressions which are shown to be accurate. Using the derived closed-form expressions, we evaluate the bit error performance of Zak-OTFS for different Tx/Rx filter configurations. Our results using Vehicular-A (Veh-A) channel model with fractional DDs show that, while matched filtering achieves slightly better or almost same performance as identical filtering, channel matched filtering achieves the best performance among the three.
title Closed-Form Expressions for I/O Relation in Zak-OTFS with Different Delay-Doppler Filters
topic Information Theory
Signal Processing
url https://arxiv.org/abs/2504.18887