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Terahertz (THz) communications are regarded as a pillar technology for the sixth generation (6G) wireless systems, by offering multi-ten-GHz bandwidth. To overcome the short transmission distance and huge propagation loss, ultra-massive (UM) MIMO systems that employ sub-millimeter wavelength antennas array are proposed to enable an enticingly high array gain. In the UM-MIMO systems, hybrid beamforming stands out for its great potential in promisingly high data rate and reduced power consumption. In this paper, challenges and features of the THz hybrid beamforming design are investigated, in light of the distinctive THz peculiarities. Specifically, we demonstrate that the spatial degree-of-freedom (SDoF) is less than 5, which is caused by the extreme sparsity of the THz channel. The blockage problem caused by the huge reflection and scattering losses, as high as 15 dB or over, is studied. Moreover, we analyze the challenges led by the array containing 1024 or more antennas, including the requirement for intelligent subarray architecture, strict energy efficiency, and propagation characterization based on spherical-wave propagation mechanisms. Owning up to hundreds of GHz bandwidth, beam squint effect could cause over 5~dB array gain loss, when the fractional bandwidth exceeds 10%. Inspired by these facts, three novel THz-specific hybrid beamforming architectures are presented, including widely-spaced multi-subarray, dynamic array-of-subarrays, and true-time-delay-based architectures. We also demonstrate the potential data rate, power consumption, and array gain capabilities for THz communications. As a roadmap of THz hybrid beamforming design, multiple open problems and potential research directions are elaborated., Comment: 7 pages

Terahertz (THz) communications with multi-GHz bandwidth are envisioned as a key technology for 6G systems. Ultra-massive (UM) MIMO with hybrid beamforming architectures are widely investigated to provide a high array gain to overcome the huge propagation loss. However, most of the existing hybrid beamforming architectures can only utilize the multiplexing offered by the multipath components, i.e., inter-path multiplexing, which is very limited due to the spatially sparse THz channel. In this paper, a widely-spaced multi-subarray (WSMS) hybrid beamforming architecture is proposed, which improves the multiplexing gain by exploiting a new type of intra-path multiplexing provided by the spherical-wave propagation among k widely-spaced subarrays, in addition to the inter-path multiplexing. The resulting multiplexing gain of WSMS architecture is k times of the existing architectures. To harness WSMS hybrid beamforming, a novel design problem is formulated by optimizing the number of subarrays, subarray spacing, and hybrid beamforming matrices to maximize the spectral efficiency, which is decomposed into two subproblems. An optimal closed-form solution is derived for the first hybrid beamforming subproblem, while a dominant-line-of-sight-relaxation algorithm is proposed for the second array configuration subproblem. Extensive simulation results demonstrate that the WSMS architecture and proposed algorithms substantially enhance the spectral efficiency and energy efficiency., Comment: 30 pages

Terahertz (THz) communications have been envisioned as a promising enabler to provide ultra-high data transmission for sixth generation (6G) wireless networks. To tackle the blockage vulnerability brought by severe path attenuation and poor diffraction of THz waves, an intelligent reflecting surface (IRS) is put forward to smartly control the incident THz waves by adjusting the phase shifts. In this paper, we firstly design an efficient hardware structure of graphene-based IRS with phase response up to 306.82 degrees. Subsequently, to characterize the capacity of the IRS-enabled THz multiple-input multiple-output (MIMO) system, an adaptive gradient descent (A-GD) algorithm is developed by dynamically updating the step size during the iterative process, which is determined by the second-order Taylor expansion formulation. In contrast with conventional gradient descent (C-GD) algorithm with fixed step size, the A-GD algorithm evidently improves the achievable rate performance. However, both A-GD algorithm and C-GD algorithm inherit the unacceptable complexity. Then a low complexity alternating optimization (AO) algorithm is proposed by alternately optimizing the precoding matrix by a column-by-column (CBC) algorithm and the phase shift matrix of the IRS by a linear search algorithm. Ultimately, the numerical results demonstrate the effectiveness of the designed hardware structure and the considered algorithms.

Software-Defined Metamaterials (SDMs) show a strong potential for advancing the engineered control of electromagnetic waves. As such, they are envisioned to enable a variety of exciting applications, among others in the domains of smart textiles, high-resolution structural monitoring, and sensing in challenging environments. Many of the applications envisage deformations of the SDM structures, such as their bending, stretching or rolling, which implies that the locations of metamaterial elements will be changing relative to one another. In this paper, we argue that if the metamaterial elements would be accurately localizable, this location information could potentially be utilized for enabling novel SDM applications, as well as for optimizing the control of the elements themselves. To enable their localization, we assume that these elements are controlled wirelessly through a Terahertz (THz)-operating nanonetwork. We consider the elements to be power-constrained, with their sole powering option being to harvest energy from different environmental sources. By means of simulation, we demonstrate sub-millimeter accuracy of the two-way Time of Flight (ToF)-based localization, as well as high availability of the service (i.e., consistently more than 80% of the time), which is a result of the low energy consumed in the localization process. Finally, we qualitatively characterize the latency of the proposed localization service, as well as outline several challenges and future research directions., Comment: 49 pages, 19 figures, 2 tables

We derive new expressions for the connection probability and the average ergodic capacity to evaluate the performance achieved by multi-connectivity (MC) in an indoor ultra-wideband terahertz (THz) communication system. In this system, the user is affected by both self-blockage and dynamic human blockers. We first build up a three-dimensional propagation channel in this system to characterize the impact of molecular absorption loss and the shrinking usable bandwidth nature of the ultra-wideband THz channel. We then carry out new performance analysis for two MC strategies: 1) Closest line-of-sight (LOS) access point (AP) MC (C-MC), and 2) Reactive MC (R- MC). With numerical results, we validate our analysis and show the considerable improvement achieved by both MC strategies in the connection probability. We further show that the C-MC and R-MC strategies provide significant and marginal capacity gain relative to the single connectivity strategy, respectively, and increasing the number of the users associated APs imposes completely different affects on the capacity gain achieved by the C-MC and R-MC strategies. Additionally, we clarify that our analysis allows us to determine the optimal density of APs in order to maximize the capacity gain., Comment: Accepted to appear in IEEE ICC 2020

Terahertz communications are envisioned as a key technology for 6G, which requires 100+ Gbps data rates, 1-millisecond latency, among other performance metrics. As a fundamental wireless infrastructure, the THz communication can boost abundant promising applications, including next-generation WLAN systems like Tera-WiFi, THz wireless backhaul, as well as other long-awaited novel communication paradigms. Serving as a basis of efficient wireless communication and networking design, this paper highlights the key THz channel features and recent advancements in device technologies. In light of these, impact and guidelines on 6G wireless communication and networking are elaborated. We believe the progress of THz technologies is helping finally close the so called THz Gap, and will realize THz communications as a pillar of 6G wireless systems.

We propose novel hybrid beamforming schemes for the terahertz (THz) wireless system where a multi-antenna base station (BS) communicates with a multi-antenna user over frequency selective fading. Here, we assume that the BS employs sub-connected hybrid beamforming and multi-carrier modulation to deliver ultra high data rate. We consider a three-dimensional wideband THz channel by incorporating the joint effect of molecular absorption, high sparsity, and multi-path fading, and consider the carrier frequency offset in multi-carrier systems. With this model, we first propose a two-stage wideband hybrid beamforming scheme which includes a beamsteering codebook searching algorithm for analog beamforming and a regularized channel inversion method for digital beamforming. We then propose a novel wideband hybrid beamforming scheme with two digital beamformers. In this scheme, an additional digital beamformer is developed to compensate for the performance loss caused by the constant-amplitude hardware constraints and the difference of channel matrices among subcarriers. Furthermore, we consider imperfect channel state information (CSI) and propose a probabilistic robust hybrid beamforming scheme to combat channel estimation errors. Numerical results demonstrate the benefits of our proposed schemes for the sake of practical implementation, especially considering its high spectral efficiency, low complexity, and robustness against imperfect CSI., Comment: 31 pages, 5 figures

In the millimeter wave (30-300 GHz) and Terahertz (0.1-10 THz) frequency bands, high spreading loss and molecular absorption often limit the signal transmission distance and coverage range. In this paper, four directions to tackle the crucial problem of distance limitation are investigated, namely, a physical layer distance-aware design, ultra-massive MIMO communication, reflectarrays, and intelligent surfaces. Additionally, the potential joint design of these technologies is proposed to combine the benefits and possibly further extend the communication distance. Qualitative analyses and quantitative simulations are provided to illustrate the benefits of the proposed techniques and demonstrate the feasibility of mm-wave and THz band communications up to 100 meters in both line-of-sight and non-line-of-sight areas.

Let $M^{2n+1}$, $n\ge 1$, be a smooth manifold with a pseudo-convex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $ M=\mathcal S_0 \supset \mathcal S_1 \supset \cdots \supset \mathcal S_{n}, $ where $\mathcal S_q$ is the set of points where the Levi-form has nullity $\ge q$. We prove that $\mathcal S_q$'s are locally given as common zero sets of the coefficients $A_j,$ $j=0,1,\ldots, q-1,$ of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$., Comment: 11 pages

Given an affine control system $\dot{\mathbf x} = f({\mathbf x}) + \sum_{j=1}^m g_j({\mathbf x}) u_j$ we present an algorithmic process of construction of submanifolds that are invariant under controls assuming that the linear span of $f, g_1, \ldots, g_m$ has constant rank. We use the method of reduction of Pfaffian systems to a largest integrable subsystem and finding the first integrals and the generalized first integrals for the vector fields., Comment: 11 pages