Instantaneous Polarimetry with Zak-OTFS

Polarimetry, which is the ability to measure the scattering response of the environment across orthogonal polarizations, is fundamental to enhancing wireless communication and radar system performance. In this paper, we utilize the Zak-OTFS modulation to enable instantaneous polarimetry within a single transmission frame. We transmit a Zak-OTFS carrier waveform and a spread carrier waveform mutually unbiased to it simultaneously over orthogonal polarizations. The mutual unbiasedness of the two waveforms enables the receiver to estimate the full polarimetric response of the scattering environment from a single received frame. Unlike existing methods for instantaneous polarimetry with computational complexity quadratic in the time-bandwidth product, the proposed method enables instantaneous polarimetry at complexity that is only sublinear in the time-bandwidth product. Via numerical simulations, we show ideal polarimetric target detection and parameter estimation results with the proposed method, with improvements in performance and computational complexity over comparable baselines.

Low-Complexity Equalization of Zak-OTFS in the Frequency Domain

4G/5G wireless standards use orthogonal frequency division multiplexing (OFDM) which is robust to frequency selectivity. Equalization is possible with a single tap filter, and low-complexity equalization makes OFDM an attractive physical layer. However the performance of OFDM degrades with mobility, since Doppler spreads introduce inter-carrier interference (ICI) between subcarriers and they are no longer orthogonal. Zak-transform based orthogonal time frequency space (Zak-OTFS) modulation has been shown to be robust to doubly selective channels. Zak-OTFS signals are formed in the delay-Doppler (DD) domain, converted to time domain (TD) for transmission and reception, then returned to the DD domain for processing. The received signal is a superposition of many attenuated copies since the doubly selective channel introduces delay and Doppler shifts. The received symbols are more difficult to equalize since they are subject to interference along both delay and Doppler axes. In this paper, we propose a new low-complexity method of equalizing Zak-OTFS in the frequency domain (FD). We derive the FD system model and show that it is unitarily equivalent to the DD system model. We show that the channel matrix in the FD is banded, making it possible to apply conjugate gradient methods to reduce the complexity of equalization. We show that complexity of FD equalization is linear in the dimension of a Zak-OTFS frame. For comparison the complexity of naive MMSE equalization is cubic in the frame dimension. Through numerical simulations we show that FD equalization of Zak-OTFS achieves similar performance as equalization in DD domain.

Zak-OTFS for Spread Spectrum Communication

An attractive feature of spread spectrum technologies such as code division multiple access (CDMA) is that it is harder to intercept or jam signals, and this feature was lost when orthogonal frequency domain modulation prevailed over CDMA in wireless standards. Legacy spread carrier waveforms are not matched to delay and Doppler shifts characteristic of 6G wireless environments, and this makes equalization very challenging. Zak-OTFS modulation is a communication framework that parameterizes the wireless channel in the delay-Doppler (DD) domain, where the parameters map directly to physical attributes of the scatterers that comprise the scattering environment. Hence, the channel can be efficiently acquired and equalized. The Zak-OTFS carrier is a pulse in the DD domain, and the Zak transform converts it to a pulse train modulated by a tone (pulsone) in the time domain. The pulsone waveform is localized rather than spread, and it suffers from high PAPR. We describe how to transform Zak-OTFS into a spread spectrum communication system, where the spread carrier waveforms have low PAPR and are matched to the delay and Doppler characteristics of the wireless channel. This transformation is realized by a unitary transform that is a generalization of the discrete affine Fourier transform. The transform maps a pulsone to a time domain waveform which yields a CAZAC sequence after sampling. The family of CAZAC sequences includes the Zadoff-Chu sequences incorporated in LTE and 5G-NR standards. We describe the end-to-end time-domain transceiver signal processing, comprising channel estimation and data demodulation, for the proposed system. We quantify system performance through BER simulations using a six-path Veh-A channel model, showing that the proposed system achieves similar uncoded BER as pulsone-based Zak-OTFS, where the PAPR of each spread carrier waveform is only 3.58 dB.

Zak-OTFS for Mutually Unbiased Sensing and Communication

Waveforms with ideal ambiguity functions are fundamental to integrated sensing and communication, to active sensing (radar), and to uplink multiple access. We describe a general method of constructing waveforms using the discrete Zak transform (DZT) to convert sequences of length $MN$ in the time domain to waveforms in the delay-Doppler (DD) domain, each of which is defined by an $M\times N$ quasi-periodic array. The DZT preserves inner products, and we show that phase coded waveforms used in radar (CAZAC sequences) determine noise-like waveforms in the DD domain, each with low Peak to Average Power Ratio. In a Zak-OTFS communication system, we show that these waveforms are mutually unbiased with respect to every carrier and use them to integrate sensing and communication as spread pilots. We view each waveform as a linear combination of Zak-OTFS carriers and show that the self-ambiguity function is supported on a discrete line in the integers modulo $MN$. The sidelobes are significantly lower than the original CAZAC sequence, and the advantage of discrete support is better localization/resolution in delay and Doppler compared with standard methods based on chirps or tones. We show that the absolute value of the cross-ambiguity function for pairs of waveforms in the same family is small and constant. This property makes the waveforms ideal preambles in the 2-step RACH protocol introduced in Release 15, 3GPP to enable grant-free multiple access. The characteristics of the cross-ambiguity function make it possible to simultaneously detect multiple preambles in the presence of mobility and delay spread.

Consensus ADMM-Based Distributed Simultaneous Imaging & Communication

This paper takes the first steps toward enabling wireless networks to perform both imaging and communication in a distributed manner. We propose Distributed Simultaneous Imaging and Symbol Detection (DSISD), a provably convergent distributed simultaneous imaging and communication scheme based on the alternating direction method of multipliers. We show that DSISD achieves similar imaging and communication performance as centralized schemes, with order-wise reduction in computational complexity. We evaluate the performance of DSISD via 2.4 GHz Wi-Fi simulations.