A Gaussian-Sinc Pulse Shaping Filter for Zak-OTFS

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.