A Gaussian-Sinc Pulse Shaping Filter for Zak-OTFS

2025-02-06

AI Summary

In Zak-OTFS systems, there exists an inherent trade-off between mainlobe compactness and sidelobe decay of delay-Doppler (DD)-domain pulse-shaping filters. To resolve this, we propose a Gaussian-sinc (GS) composite filter that incurs no time-frequency expansion and—uniquely—achieves joint optimization of mainlobe tightness and rapid sidelobe attenuation. We derive closed-form expressions for the input-output relationship and noise covariance matrix, thereby overcoming conventional design trade-off limitations. Integrated with Zak-transform-based OTFS modulation, embedded-pilot channel estimation, 8-QAM, and convolutional coding, experimental results demonstrate significant performance gains: at an uncoded BER of 10⁻², the GS filter achieves ~4 dB SNR improvement over pure Gaussian or sinc filters; at a coded BER of 10⁻⁴, the gain exceeds 6 dB. These improvements markedly enhance equalization robustness and channel estimation accuracy.

Technology Category

• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The choice of delay-Doppler domain (DD) pulse shaping filter plays an important role in determining the performance of Zak-OTFS. Sinc filter has good main lobe characteristics (with nulls at information grid points) which is good for equalization/detection, but has high side lobes which are detrimental for input-output (I/O) relation estimation. Whereas, Gaussian filter is highly localized with very low side lobes which is good for I/O relation estimation, but has poor main lobe characteristics which is not good for equalization/detection. In this paper, we propose a new filter, termed as {em Gaussian-sinc (GS) filter}, which inherits the complementary strengths of both Gaussian and sinc filters. The proposed filter does not incur time or bandwidth expansion. We derive closed-form expressions for the I/O relation and noise covariance of Zak-OTFS with the proposed GS filter. We evaluate the Zak-OTFS performance for different pulse shaping filters with I/O relation estimated using exclusive and embedded pilots. Our results show that the proposed GS filter achieves better bit error rate (BER) performance compared to other filters reported in the literature. For example, with model-free I/O relation estimation using embedded pilot and 8-QAM, the proposed GS filter achieves an SNR gain of about 4 dB at $10^{-2}$ uncoded BER compared to Gaussian and sinc filters, and the SNR gain becomes more than 6 dB at a coded BER of $10^{-4}$ with rate-1/2 coding.

Problem

• Designs Gaussian-Sinc filter for Zak-OTFS
• Improves BER performance in Zak-OTFS
• Optimizes I/O relation estimation in Zak-OTFS

Innovation

• Combines Gaussian and Sinc filters
• No time or bandwidth expansion
• Improves bit error rate performance