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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2504.18887 |
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| _version_ | 1866915261600235520 |
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| 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 |