Topological quantum phase transition in an S=2 spin chain

We construct a model Hamiltonian for S = 2 spin chain, where a variable parameter $\alpha$ is introduced. The edge spin is S = 1 for $\alpha = 0$, and S = 3/2 for $\alpha = 1$. Due to the topological distinction of the edge states, these two phases must be separated by one or several topological quantum phase transitions. We investigate the nature of the quantum phase transition by DMRG calculation, and propose a phase diagram for this model.Comment: 5 pages, 4 figure

3D Channel Tracking in Space-Air-Ground Integrated Networks.

PhD ThesesThe space-air-ground integrated network (SAGIN) aims to provide seamless wide-area connections, high throughput and strong resilience for beyond the fth generation (B5G) and future communications. As a multidimensional network, SAGIN adopts di erent communication links across three segments: the space segment with satellite networks, the air segment with aerial networks, and the ground segment with territorial networks. Apart from Ka-band millimetre wave (mmWave) frequencies being utilized for low earth orbit (LEO) satellites and medium earth orbit (MEO) satellites communications, with emerging smart devices brought online and crowded under-6GHz spectrum, mmWave frequencies have also been widely considered to support both aerial networks and territorial networks. To ensure stable wireless communications and tackle the severer propagation loss of mmWave transmission, massive multiple input and multiple output (MIMO) and intelligent re ecting surfaces (IRSs), which can con gure directional beams and bring huge improvements of radiated energy e ciency, are two technologies to be employed in SAGIN. Conventionally, perfect channel state information (CSI) is the fundamental knowledge to enable building reliable communication connections. With massive antenna arrays installed on orbiting satellites, navigation unmanned aerial vehicles (UAVs), and base stations, it's very challenging to acquire real-time mmWave CSI in SAGIN due to the heavy overheads and the dynamic environment. Most existing mmWave channel estimation work proposed compressive sensing (CS) based algorithms to reduce the heavy overheads with the assumption that the environment is in two-dimensional (2D) space and static without any movement. However, in SAGIN, 2D and static assumptions are not practical. Hence, tracking the dynamic three-dimensional (3D) CSI using small training overheads becomes a crucial and demanding task. i In this thesis, 3D channel tracking algorithms are proposed based on unique characteristics of air-ground and space-air links. For IRS-assisted air-ground links, we propose a 3D geometry dynamic channel model with both UAV navigation and mobile user movement. We further develop a deep learning (DL)-based channel tracking algorithms with two modules: deep neural network (DNN) channel pre-estimation for denoising and stacked bi-directional long short term memory (Stacked Bi-LSTM) for channel tracking. For space-air links, we exploit the on-grid and o -grid single user (SU) and multi-user (MU) UAV-satellite communications. Two statistical spatial and temporal correlation sparsity of the dynamic channel models called 3D two-dimensional Markov model (3D- 2D-MM) and multi-dimensional Markov model (MD-MM) are developed by introducing the more realistic 3D movement in the system. Based on the message passing rule and the proposed Markov structures, 3D dynamic turbo approximate message passing algorithm (3D-DTAMP) and multi-dimensional dynamic turbo approximate message passing (MD-DTAMP) are derived for channel tracking. Our proposed algorithms can achieve better channel estimation accuracy with comparable complexity and smaller training overheads

6G Mobile-Edge Empowered Metaverse: Requirements, Technologies, Challenges and Research Directions

The Metaverse has emerged as the successor of the conventional mobile internet to change people's lifestyles. It has strict visual and physical requirements to ensure an immersive experience (i.e., high visual quality, low motion-to-photon latency, and real-time tactile and control experience). However, the current communication systems fall short to satisfy these requirements. Mobile edge computing (MEC) has been indispensable to enable low latency and powerful computing. Moreover, the sixth generation (6G) networks promise to provide end users with high-capacity communications to MEC servers. In this paper, we bring together the primary components into a 6G mobile-edge framework to empower the Metaverse. This includes the usage of heterogeneous radios, intelligent reflecting surfaces (IRS), non-orthogonal multiple access (NOMA), and digital twins (DTs). We also discuss novel communication paradigms (i.e., semantic communication, holographic-type communication, and haptic communication) to further satisfy the demand for human-type communications and fulfil user preferences and immersive experiences in the Metaverse

Bi-directional Digital Twin and Edge Computing in the Metaverse

The Metaverse has emerged to extend our lifestyle beyond physical limitations. As essential components in the Metaverse, digital twins (DTs) are the digital replicas of physical items. DTs enable emulation of real-world scenarios and prediction for energy and resource-efficient operation, resulting in sustainable applications. End users access the Metaverse using a variety of devices (e.g., head-mounted devices (HMDs)), mostly lightweight. Multi-access edge computing (MEC) provides responsive services to the end users, leading to an immersive Metaverse experience. With the anticipation to represent physical objects, end users, and edge computing systems as DTs in the Metaverse, the construction of these DTs and the interplay between them have not been investigated. In this paper, we discuss the bidirectional reliance between the DT and the MEC system and investigate the creation of DTs of objects and users on the MEC servers and DT-assisted edge computing (DTEC). We also study the interplay between the DTs and DTECs to allocate the resources fairly and optimally and provide an immersive experience in the Metaverse. Owing to the dynamic network states (e.g., channel states) and mobility of the users, we discuss the interplay between local DTECs (on local MEC servers) and the global DTEC (on cloud server) to cope with the handover among MEC servers and avoid intermittent Metaverse services