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Temporal knowledge graph (TKG) reasoning predicts future events based on historical data, but it's challenging due to the complex semantic and hierarchical information involved. Existing Euclidean models excel at capturing semantics but struggle with hierarchy. Conversely, hyperbolic models manage hierarchical features well but fail to represent complex semantics due to limitations in shallow models' parameters and the absence of proper normalization in deep models relying on the L2 norm. Current solutions, as curvature transformations, are insufficient to address these issues. In this work, a novel hybrid geometric space approach that leverages the strengths of both Euclidean and hyperbolic models is proposed. Our approach transitions from single-space to multi-space parameter modeling, effectively capturing both semantic and hierarchical information. Initially, complex semantics are captured through a fact co-occurrence and autoregressive method with normalizations in Euclidean space. The embeddings are then transformed into Tangent space using a scaling mechanism, preserving semantic information while relearning hierarchical structures through a query-candidate separated modeling approach, which are subsequently transformed into Hyperbolic space. Finally, a hybrid inductive bias for hierarchical and semantic learning is achieved by combining hyperbolic and Euclidean scoring functions through a learnable query-specific mixing coefficient, utilizing embeddings from hyperbolic and Euclidean spaces. Experimental results on four TKG benchmarks demonstrate that our method reduces error relatively by up to 15.0% in mean reciprocal rank on YAGO compared to previous single-space models. Additionally, enriched visualization analysis validates the effectiveness of our approach, showing adaptive capabilities for datasets with varying levels of semantic and hierarchical complexity.

Compared to passive intelligent reflecting surface (IRS), active IRS is viewed as a more efficient promising technique to combat the double-fading impact in IRS-aided wireless network. In this paper, in order to boost the achievable rate of user in such a wireless network, three enhanced-rate iterative beamforming methods are proposed by designing the amplifying factors and the corresponding phases at active IRS. The first method, maximizing the simplified signal-to-noise ratio (Max-SSNR) is designed by omitting the cross-term in the definition of rate. Using the Rayleigh-Ritz (RR) theorem, Max-SSNR-RR is proposed to iteratively optimize the norm of beamforming vector and its associated normalized vector. In addition, generalized maximum ratio reflection (GMRR) is presented with a closed-form expression, which is motivated by the maximum ratio combining. To further improve rate, maximizing SNR (Max-SNR) is designed by fractional programming (FP), which is called Max-SNR-FP. Simulation results show that the proposed three methods make an obvious rate enhancement over Max-reflecting signal-to-noise ratio (Max-RSNR), maximum ratio reflection (MRR), selective ratio reflecting (SRR), equal gain reflection (EGR) and passive IRS, and are in increasing order of rate performance as follows: Max-SSNR-RR, GMRR, and Max-SNR-FP.

In this paper, with the help of an intelligent reflecting surface (IRS), the source (S) and destination (D) exchange information through the two-way decode-and-forward relay (TW-DFR). We mainly focus on the phase optimization of IRS to improve the system rate performance. Firstly, a maximizing receive power sum (Max-RPS) method is proposed via eigenvalue decomposition (EVD) with an appreciable rate enhancement, which is called Max-RPS-EVD. To further achieve a higher rate, a method of maximizing minimum rate (Max-Min-R) is proposed with high complexity. To reduce its complexity, a low-complexity method of maximizing the sum rate (Max-SR) via general power iterative (GPI) is proposed, which is called Max-SR-GPI. Simulation results show that the proposed three methods outperform the case of random phase method, especially the proposed Max-SR-GPI method is the best one achieving at least 20\% rate gain over random phase. Additionally, it is also proved the optimal rate can be achieved when TW-DFR and IRS are located in the middle of S and D., Comment: 9 pages,10 figures

In this paper, we investigate the problem of pilot optimization and channel estimation of two-way relaying network (TWRN) aided by an intelligent reflecting surface (IRS) with finite discrete phase shifters. In a TWRN, there exists a challenging problem that the two cascading channels from source-to-IRS-to-Relay and destination-to-IRS-to-relay interfere with each other. Via designing the initial phase shifts of IRS and pilot pattern, the two cascading channels are separated by using simple arithmetic operations like addition and subtraction. Then, the least-squares estimator is adopted to estimate the two cascading channels and two direct channels from source to relay and destination to relay. The corresponding mean square errors (MSE) of channel estimators are derived. By minimizing MSE, the optimal phase shift matrix of IRS is proved. Then, two special matrices Hadamard and discrete Fourier transform (DFT) matrix is shown to be two optimal training matrices for IRS. Furthermore, the IRS with discrete finite phase shifters is taken into account. Using theoretical derivation and numerical simulations, we find that 3-4 bits phase shifters are sufficient for IRS to achieve a negligible MSE performance loss. More importantly, the Hadamard matrix requires only one-bit phase shifters to achieve the optimal MSE performance while the DFT matrix requires at least three or four bits to achieve the same performance. Thus, the Hadamard matrix is a perfect choice for channel estimation using low-resolution phase-shifting IRS., Comment: 5 pages, 5 figures

As massive multiple-input multiple-output (MIMO) becomes popular, direction of arrival (DOA) measurement has been made a real renaissance due to the high-resolution achieved. Thus, there is no doubt about DOA estimation using massive MIMO. The purpose of this paper is to describe its basic principles and key techniques, to present the performance analysis, and to appreciate its engineering applications. It is anticipated that there are still many challenges in DOA estimation using massive receive MIMO, such as high circuit cost, high energy consumption and high complexity of the algorithm implementation. New researches and breakthroughs are illustrated to deal with those problems. Then, a new architecture, hybrid analog and digital (HAD) massive receive MIMO with low-resolution ADCs, is presented to strike a good balance among circuit cost, complexity and performance. Then, a novel three-dimensional (3D) angle of arrival (AOA) localization method based on geometrical center is proposed to compute the position of a passive emitter using single base station equipped with an ultra-massive MIMO system. And, it can achieve the Cramer-Rao low bound (CRLB). Here, the performance loss is also analyzed to quantify the minimum number of bits. DOA estimation will play a key role in lots of applications, such as directional modulation, beamforming tracking and alignment for 6G.