Core Concepts
Gaussian pulse shaping filters in the delay-Doppler domain improve the predictability and performance of Zak-OTFS modulation compared to sinc and root raised cosine filters.
Abstract
The key highlights and insights from the content are:
Zak-OTFS is a modulation scheme that separates reflections in both range and velocity, making it suitable for 6G propagation environments with extreme Doppler spreads. The Zak-OTFS input-output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition referred to as the crystallization condition.
The authors introduce a framework for filter design in the delay-Doppler (DD) domain, where the symplectic Fourier transform connects aliasing in the DD domain (predictability of the I/O relation) with time/bandwidth expansion.
The authors propose integrating sensing and communication within a single Zak-OTFS subframe by transmitting a pilot in the center and surrounding it with a pilot region and guard band to mitigate interference between data symbols and pilot.
Gaussian pulse shaping filters in the DD domain provide significant improvements in BER performance over the sinc and root raised cosine (RRC) filters considered in previous work. Gaussian filters also extend the region where the crystallization condition is satisfied.
The choice of pulse shaping filter determines the fraction of pilot energy that lies outside the pilot region and the degradation in BER performance that results from the interference to data symbols. Gaussian filters have very little leakage outside the main lobe, resulting in minimal interference from the pilot.
The design of factorizable pulse shaping filters in the delay-Doppler domain may be of independent interest, as the time and bandwidth properties of the carrier waveforms follow naturally from the Fourier properties of the factors.
Stats
The power-delay profile of the Veh-A channel model used in the simulations is provided in Table I.
Quotes
"The Zak-OTFS input/output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition which we refer to as the crystallization condition."
"Gaussian filters in the DD domain provide significant improvements in BER performance over the sinc and root raised cosine (RRC) filters considered in previous work."
"Gaussian filters limit aliasing in the delay-Doppler domain, and this translates to increasing the length of the segment of the period curve where the crystallization conditions are satisfied."