Hai Lin

The recently proposed orthogonal delay-Doppler division multiplexing (ODDM) modulation, which is a delay-Doppler (DD) domain multi-carrier (DDMC) modulation scheme based on the DD domain orthogonal pulse (DDOP), is studied. We first revisit the linear time-varying (LTV) channel model for the wireless channel, and review the conventional multi-carrier (MC) modulation schemes and their design guidelines for both linear time-invariant (LTI) and LTV channels. We then focus on the representation of the LTV channel in an equivalent sampled DD (ESDD) domain, and propose an impulse-function-based transmission strategy for the ESDD channel. Next, we take an in-depth look into the DDOP and show that it achieves orthogonality with respect to the fine time and frequency resolutions in the ESDD domain thus behaves like an impulse function. This allows us to unveil the unique input-output relation of the resultant ODDM modulation over the ESDD channel. We point out that the conventional MC modulation design guidelines based on the Weyl-Heisenberg (WH) frame theory can be relaxed without compromising its orthogonality or violating the WH frame theory. More specifically, for a practical communication system with bandwidth and duration constraints, MC modulation signals can be designed considering so-called local or sufficient (bi)orthogonality, which refers to the (bi)orthogonality among a WH subset for the MC signal within a specific bandwidth and duration. This is different from the conventional MC modulation waveform design guidelines (such as for orthogonal frequency division multiplexing and orthogonal time frequency space) based on the global (bi)orthogonality, which is the (bi)orthogonality among a WH full set corresponding to the MC signal occupying the entire TF domain. This novel design guideline could potentially open up opportunities for developing future waveforms required by new applications such as communication systems associated with high delay and/or Doppler shifts, as well as integrated sensing and communications.

In this paper, we propose to employ a modular-based movable extremely large-scale array (XL-array) at Alice for enhancing covert communication performance. Compared with existing work that mostly considered either far-field or near-field covert communications, we consider in this paper a more general and practical mixed-field scenario, where multiple Bobs are located in either the near-field or far-field of Alice, in the presence of multiple near-field Willies. Specifically, we first consider a two-Bob-one-Willie system and show that conventional fixed-position XL-arrays suffer degraded sum-rate performance due to the energy-spread effect in mixed-field systems, which, however, can be greatly improved by subarray movement. On the other hand, for transmission covertness, it is revealed that sufficient angle difference between far-field Bob and Willie as well as adequate range difference between near-field Bob and Willie are necessary for ensuring covertness in fixed-position XL-array systems, while this requirement can be relaxed in movable XL-array systems thanks to flexible channel correlation control between Bobs and Willie. Next, for general system setups, we formulate an optimization problem to maximize the achievable weighted sum-rate under covertness constraint. To solve this non-convex optimization problem, we first decompose it into two subproblems, corresponding to an inner problem for beamforming optimization given positions of subarrays and an outer problem for subarray movement optimization. Although these two subproblems are still non-convex, we obtain their high-quality solutions by using the successive convex approximation technique and devising a customized differential evolution algorithm, respectively. Last, numerical results demonstrate the effectiveness of proposed movable XL-array in balancing sum-rate and covert communication requirements, as compared to various benchmark schemes.

The delay- Doppler (DD) domain modulation has been regarded as one of the most competitive candidates to support wireless communications for emerging high-mobility applications in the sixth-generation mobile networks. Unfortunately, most of the existing designs for DD domain modulation suffer from high peak-to-average power ratio (PAPR) and unbearable detection complexity under uplink transmission since large time duration and bandwidth are required to guarantee high DD resolutions. To address these issues, the Doppler shift keying (DSK) modulation based on the orthogonal delay Doppler division multiplexing modulator is proposed in this paper, where the input-output characterization in the DD domain is fully exploited. The principle of the DSK transceiver is first established with the one-hot mapper and low-complexity iterative successive interference cancellation-maximum ratio combining detector for point-to-point scenarios. The proposed scheme is then generalized to the zero auto-correlation sequence-based implementation, which benefits the extension of multi-user (MU) uplink DSK frameworks. For uplink DSK transmission, Zadoff-Chu (ZC) sequences are adopted as the basis sequences. We optimize the assignment of ZC roots to different user equipments (UEs) by minimizing the maximum inter-user interference. This optimization process, which analyzes the root allocation, directly assigns a specific ZC sequence to each UE. The PAPR and bit error rate performance of the proposed DSK modulation with the low-complexity detector is finally verified by extensive simulation results under doubly-dispersive channels, which demonstrates the superiority of DSK modulation especially for uplink multiple access over doubly dispersive channels.

Orthogonal delay-Doppler division multiplexing (ODDM) is a promising modulation technique for reliable communications in high-mobility scenarios. However, the existing channel estimation frameworks for ODDM systems cannot achieve both high accuracy and low complexity simultaneously, due to the inherent coupling of delay and Doppler parameters. To address this problem, a two-dimensional (2D) hierarchical sparse Bayesian learning (HSBL) based channel estimation framework is proposed in this paper. Specifically, we address the inherent coupling between delay and Doppler dimensions in ODDM by developing a partially-decoupled 2D sparse signal recovery (SSR) formulation on a virtual sampling grid defined in the delay-Doppler (DD) domain. With the help of the partially-decoupled formulation, the proposed 2D HSBL framework first performs low-complexity coarse on-grid 2D sparse Bayesian learning (SBL) estimation to identify potential channel paths. Then, high-resolution fine grids are constructed around these regions, where an off-grid 2D SBL estimation is applied to achieve accurate channel estimation. Simulation results demonstrate that the proposed framework achieves performance superior to conventional off-grid 2D SBL with significantly reduced computational complexity.

This paper proposes a new orthogonal delay-Doppler division multiplexing (ODDM) system, which is designed to operate without the need of using a cyclic prefix (CP) in the transmitted signals. The CP-free ODDM is enabled by exploiting the unique structures of the ODDM prototype pulses, which are constructed through repetitions of finite-duration elementary pulses. The system eliminates the need of CP by designing a new receiving filter through temporally extending the transmission prototype pulse. The elementary pulse repetition at the transmitter along with the temporal filter extension at the receiver introduce a wrap-around effect in the equivalent channel spreading function in the dealy-Doppler (DD) domain. The wrap-around effect leads to a block-circulant-like structure of the DD-domain channel matrix that is the same as conventional ODDM systems with CP. Thus CP-free ODDM can employ the same receiver as conventional ODDM systems, yet it yields a higher energy efficiency as no energy needs to be allocated for CP symbols. The wrap-around effects are theoretically demonstrated by deriving the exact analytical expressions of the cross-ambiguity functions of practical transmission and receiving prototype pulses. In addition, theoretical analysis of the cross-ambiguity function verifies that the CP-free ODDM waveforms satisfy local bi-orthogonality in the delay and Doppler domains. This bi-orthogonality property along with the wrap-around effects of the channel spreading function enables the design of a low complexity iterative receiver, which performs interference cancellation and coherent matrix combining (CMC) in the delay domain and minimum mean squared error (MMSE) detection in the Doppler domain. The proposed receiver can collect the diversity in both the delay and Doppler domains while simultaneously suppressing the negative impacts of DD-domain intersymbol interference (ISI) introduced by the doubly-selective fading channels.

In this paper, we propose to employ a modular-based movable extremely large-scale array (XL-array) at Alice for enhancing covert communication performance. Compared with existing work that mostly considered either far-field or near-field covert communications, we consider in this paper a more general and practical mixed-field scenario, where multiple Bobs are located in either the near-field or far-field of Alice, in the presence of multiple near-field Willies. Specifically, we first consider a two-Bob-one-Willie system and show that conventional fixed-position XL-arrays suffer degraded sum-rate performance due to the energy-spread effect in mixed-field systems, which, however, can be greatly improved by subarray movement. On the other hand, for transmission covertness, it is revealed that sufficient angle difference between far-field Bob and Willie as well as adequate range difference between near-field Bob and Willie are necessary for ensuring covertness in fixed-position XL-array systems, while this requirement can be relaxed in movable XL-array systems thanks to flexible channel correlation control between Bobs and Willie. Next, for general system setups, we formulate an optimization problem to maximize the achievable sum-rate under covertness constraint. To solve this non-convex optimization problem, we first decompose it into two subproblems, corresponding to an inner problem for beamforming optimization given positions of subarrays and an outer problem for subarray movement optimization. Although these two subproblems are still non-convex, we obtain their high-quality solutions by using the successive convex approximation technique and devising a customized differential evolution algorithm, respectively. Last, numerical results demonstrate the effectiveness of proposed movable XL-array in balancing sum-rate and covert communication requirements.

Delay-Doppler (DD) domain modulation such as orthogonal DD division multiplexing (ODDM) has been recently explored for communications over doubly selective channels. This paper derives equivalent sampled (on-grid) DD (ESDD) channel models for the effective discrete-time channels in ODDM systems over highly-spread off-grid physical channels with delay and Doppler shifts that can exceed the subpulse spacing and subtone spacing, respectively, of the DD orthogonal pulse (DDOP). The derived ESDD models account for i) off-grid delay and Doppler shifts present in practical physical channels, ii) sample-wise pulse shaping at the transmitter, and iii) matched filtering and windowing at the receiver. We then investigate the supports of the ESDD models and their implications on the input-output (IO) relation of ODDM adopting more general pulses and windows over highly-spread physical channels. In particular, we show that the digital sequences of ODDM couple finely with on-grid discrete-time DD channels, which leads to compact IO relation. We also analyze the folding and aliasing of the ESDD channel and their influence on the fading effect and predictability of effective channels experienced by the DD-domain symbols of ODDM. Based on the results, we identify conditions under which the ESDD channels can be estimated directly from embedded DD-domain pilots in a single ODDM frame. Finally, numerical results are provided to further demonstrate the findings of this paper.