U-shaped Transformer: Retain High Frequency Context in Time Series Analysis

Time series prediction plays a crucial role in various industrial fields. In recent years, neural networks with a transformer backbone have achieved remarkable success in many domains, including computer vision and NLP. In time series analysis domain, some studies have suggested that even the simplest MLP networks outperform advanced transformer-based networks on time series forecast tasks. However, we believe these findings indicate there to be low-rank properties in time series sequences. In this paper, we consider the low-pass characteristics of transformers and try to incorporate the advantages of MLP. We adopt skip-layer connections inspired by Unet into traditional transformer backbone, thus preserving high-frequency context from input to output, namely U-shaped Transformer. We introduce patch merge and split operation to extract features with different scales and use larger datasets to fully make use of the transformer backbone. Our experiments demonstrate that the model performs at an advanced level across multiple datasets with relatively low cost

Note on the Persistence of a Nonautonomous Lotka-Volterra Competitive System with Infinite Delay and Feedback Controls

We study a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls. We establish a series of criteria under which a part of n-species of the systems is driven to extinction while the remaining part of the species is persistent. Particularly, as a special case, a series of new sufficient conditions on the persistence for all species of system are obtained. Several examples together with their numerical simulations show the feasibility of our main results

306-321 GHz Wideband Channel Measurement and Analysis in an Indoor Lobby

The Terahertz (0.1-10 THz) band has been envisioned as one of the promising spectrum bands to support ultra-broadband sixth-generation (6G) and beyond communications. In this paper, a wideband channel measurement campaign in an indoor lobby at 306-321 GHz is presented. The measurement system consists of a vector network analyzer (VNA)-based channel sounder, and a directional antenna equipped at the receiver to resolve multi-path components (MPCs) in the angular domain. In particular, 21 positions and 3780 channel impulse responses (CIRs) are measured in the lobby, including the line-of-sight (LoS), non-line-of-sight (NLoS) and obstructed-line-of-sight (OLoS) cases. Multi-path propagation is elaborated in terms of clustering results, and the effect of typical scatterers in the indoor lobby scenario in the THz band is explored. Moreover, indoor THz channel characteristics are analyzed in depth. Specifically, best direction and omni-directional path losses are analyzed by invoking close-in and alpha-beta path loss models. The most clusters are observed in the OLoS case, followed by NLoS and then LoS cases. On average, the power dispersion of MPCs is smaller in the LoS case in both temporal and angular domains, compared with the NLoS and OLoS counterparts.Comment: 6 pages, 15 figure

Channel Measurement and Characterization with Modified SAGE Algorithm in an Indoor Corridor at 300 GHz

The much higher frequencies in the Terahertz (THz) band prevent the effective utilization of channel models dedicated for microwave or millimeter-wave frequency bands. In this paper, a measurement campaign is conducted in an indoor corridor scenario at 306-321 GHz with a frequency-domain Vector Network Analyzer (VNA)-based sounder. To realize high-resolution multipath component (MPC) extraction for the direction-scan measurement campaigns in the THz band, a novel modified space-alternating generalized expectation-maximization (SAGE) algorithm is further proposed. Moreover, critical channel characteristics, including the path loss, shadow fading, K-factor, delay spread, angular spreads, cluster parameters, and cross correlations are calculated and analyzed in the LoS case. Besides, two contrasted measurement campaigns in the NLoS case are conducted, with and without additional reflective foils on walls to serve as effective scatterers. Comparison results indicate that the reflective foils are useful to improve the channel conditions in the NLoS case by nearly 6 dB, which is potential to be utilized as alternative of intelligent reflecting surfaces (IRS) to enhance the coverage ability of THz communications.Comment: 12 pages, 8 figure

300 GHz Channel Measurement and Characterization in the Atrium of a Building

With abundant bandwidth resource, the Terahertz band (0.1~THz to 10~THz) is envisioned as a key technology to realize ultra-high data rates in the 6G and beyond mobile communication systems. However, moving to the THz band, existing channel models dedicated for microwave or millimeter-wave bands are ineffective. To fill this research gap, extensive channel measurement campaigns and characterizations are necessary. In this paper, using a frequency-domain Vector Network Analyzer (VNA)-based sounder, a measurement campaign is conducted in the outdoor atrium of a building in 306-321 GHz band. The measured data are further processed to obtain the channel transfer functions (CTFs), parameters of multipath components (MPCs), as well as clustering results. Based on the MPC parameters, the channel characteristics, such as path loss, shadow fading, K-factor, etc., are calculated and analyzed. The extracted channel characteristics and numerology are helpful to study channel modeling and guide system design for THz communications.Comment: 5 pages, 2 figures. arXiv admin note: text overlap with arXiv:2203.16745 by other author

Terahertz Channel Measurement and Analysis on a University Campus Street

Owning abundant bandwidth resource, the Terahertz (0.1-10 THz) band is a promising spectrum to support sixth-generation (6G) and beyond communications. As the foundation of channel study in the spectrum, channel measurement is ongoing in covering representative 6G communication scenarios and promising THz frequency bands. In this paper, a wideband channel measurement in an L-shaped university campus street is conducted at 306-321 GHz and 356-371 GHz. In particular, ten line-of-sight (LoS) and eight non-line-of-sight (NLoS) points are measured at the two frequency bands, respectively. In total, 6480 channel impulse responses (CIRs) are obtained from the measurement, based on which multi-path propagation in the L-shaped roadway in the THz band is elaborated to identify major scatterers of walls, vehicles, etc. in the environment and their impact on multi-path components (MPCs). Furthermore, outdoor THz channel characteristics in the two frequency bands are analyzed, including path losses, shadow fading, cluster parameters, delay spread and angular spread. In contrast with the counterparts in the similar outdoor scenario at lower frequencies, the results verify the sparsity of MPCs at THz frequencies and indicate smaller power spreads in both temporal and spatial domains in the THz band.Comment: 6 pages, 15 figure

300 GHz Dual-Band Channel Measurement, Analysis and Modeling in an L-shaped Hallway

The Terahertz (THz) band (0.1-10 THz) has been envisioned as one of the promising spectrum bands for sixth-generation (6G) and beyond communications. In this paper, a dual-band angular-resolvable wideband channel measurement in an indoor L-shaped hallway is presented and THz channel characteristics at 306-321 GHz and 356-371 GHz are analyzed. It is found that conventional close-in and alpha-beta path loss models cannot take good care of large-scale fading in the non-line-of-sight (NLoS) case, for which a modified alpha-beta path loss model for the NLoS case is proposed and verified in the NLoS case for both indoor and outdoor L-shaped scenarios. To describe both large-scale and small-scale fading, a ray-tracing (RT)-statistical hybrid channel model is proposed in the THz hallway scenario. Specifically in the hybrid model, the deterministic part in hybrid channel modeling uses RT modeling of dominant multi-path components (MPCs), i.e., LoS and multi-bounce reflected paths in the near-NLoS region, while dominant MPCs at far-NLoS positions can be deduced based on the developed statistical evolving model. The evolving model describes the continuous change of arrival angle, power and delay of dominant MPCs in the NLoS region. On the other hand, non-dominant MPCs are generated statistically. The proposed hybrid approach reduces the computational cost and solves the inaccuracy or even missing of dominant MPCs through RT at far-NLoS positions