This paper introduces a new two-dimensional modulation technique called Orthogonal Time Frequency Space (OTFS) modulation. OTFS has the novel and important feature of being designed in the delay-Doppler domain. When coupled with a suitable equalizer, OTFS modulation is able to exploit the full channel diversity over both time and frequency. Moreover, it converts the fading, time-varying wireless channel experienced by modulated signals such as OFDM into a time-independent channel with a complex channel gain that is essentially constant for all symbols.This design obviates the need for transmitter adaptation, and greatly simplifies system operation. The paper describes the basic operating principles of OTFS as well as a possible implementation as an overlay to current or anticipated standardized systems. OTFS is shown to provide significant performance improvement in systems with high Doppler, short packets, and/or large antenna array. In particular, simulation results indicate at least several dB of block error rate performance improvement for OTFS over OFDM in all of these settings.
The cryo-electron microscopy (cryo-EM) reconstruction problem is to find the three-dimensional structure of a macromolecule given noisy versions of its two-dimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryo-EM images of nearby viewing angles. This identification is an important first step in three-dimensional structure determination of macromolecules from cryo-EM, because once identified, these images can be rotationally aligned and averaged to produce “class averages” of better quality. The main advantage of our algorithm is its extreme robustness to noise. The algorithm is also very efficient in terms of running time and memory requirements, because it is based on the computation of the top few eigenvectors of a specially designed sparse Hermitian matrix. These advantages are demonstrated in numerous numerical experiments.
The sixth-generation (6G) wireless networks are envisioned to provide a global coverage for the intelligent digital society of the near future, ranging from traditional terrestrial to non-terrestrial networks, where reliable communications in highmobility scenarios at high carrier frequencies would play a vital role. In such scenarios, the conventional orthogonal frequency division multiplexing (OFDM) modulation, that has been widely used in both the fourth-generation (4G) and the emerging fifthgeneration (5G) cellular systems as well as in WiFi networks, is vulnerable to severe Doppler spread. In this context, this article aims to introduce a recently proposed two-dimensional modulation scheme referred to as orthogonal time-frequency space (OTFS) modulation, which conveniently accommodates the channel dynamics via modulating information in the delay-Doppler domain. This article provides an easy-reading overview of OTFS, highlighting its underlying motivation and specific features. The critical challenges of OTFS and our preliminary results are presented. We also discuss a range of promising research opportunities and potential applications of OTFS in 6G wireless networks.
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