Riemannian Manifold Optimization for Advanced Wireless Communications: Fundamentals and Applications

Next-generation wireless communications promise transformative technologies such as massive multiple-input multiple-output (MIMO), reconfigurable intelligent surfaces (RIS), integrated sensing and communication (ISAC), and fluid antenna systems (FAS). However, deploying these technologies is hindered by large-scale optimization problems with nonconvex constraints. Conventional Euclidean-space methods rely on approximations or relaxations, which degrade performance and incur substantial computational costs. Riemannian manifold optimization (RMO) offers a powerful alternative that directly operates on the manifold defined by the geometric constraints. This approach inherently satisfies the constraints at every optimization step, thereby avoiding the performance degradation and substantial computational costs. In this paper, we first elaborate on the principles of RMO, including the fundamental concepts, tools, and methods, emphasizing its effectiveness for nonconvex problems. We then introduce its applications in advanced wireless communications, showing how constrained problems are reformulated on their natural manifolds and solved using tailored RMO algorithms. Furthermore, we present a case study on secure beamforming in an FAS-assisted non-orthogonal multiple access (NOMA) system, demonstrating RMO's superiority over conventional methods in terms of both performance and computational efficiency.

Wireless Context Engineering for Efficient Mobile Agentic AI and Edge General Intelligence

Future wireless networks demand increasingly powerful intelligence to support sensing, communication, and autonomous decision-making. While scaling laws suggest improving performance by enlarging model capacity, practical edge deployments are fundamentally constrained by latency, energy, and memory, making unlimited model scaling infeasible. This creates a critical need to maximize the utility of limited inference-time inputs by filtering redundant observations and focusing on high-impact data. In large language models and generative artificial intelligence (AI), context engineering has emerged as a key paradigm to guide inference by selectively structuring and injecting task-relevant information. Inspired by this success, we extend context engineering to wireless systems, providing a systematic way to enhance edge AI performance without increasing model complexity. In dynamic environments, for example, beam prediction can benefit from augmenting instantaneous channel measurements with contextual cues such as user mobility trends or environment-aware propagation priors. We formally introduce wireless context engineering and propose a Wireless Context Communication Framework (WCCF) to adaptively orchestrate wireless context under inference-time constraints. This work provides researchers with a foundational perspective and practical design dimensions to manage the wireless context of wireless edge intelligence. An ISAC-enabled beam prediction case study illustrates the effectiveness of the proposed paradigm under constrained sensing budgets.

Low-Complexity Distributed Combining Design for Near-Field Cell-Free XL-MIMO Systems

In this paper, we investigate the low-complexity distributed combining scheme design for near-field cell-free extremely large-scale multiple-input-multiple-output (CF XL-MIMO) systems. Firstly, we construct the uplink spectral efficiency (SE) performance analysis framework for CF XL-MIMO systems over centralized and distributed processing schemes. Notably, we derive the centralized minimum mean-square error (CMMSE) and local minimum mean-square error (LMMSE) combining schemes over arbitrary channel estimators. Then, focusing on the CMMSE and LMMSE combining schemes, we propose five low-complexity distributed combining schemes based on the matrix approximation methodology or the symmetric successive over relaxation (SSOR) algorithm. More specifically, we propose two matrix approximation methodology-aided combining schemes: Global Statistics \& Local Instantaneous information-based MMSE (GSLI-MMSE) and Statistics matrix Inversion-based LMMSE (SI-LMMSE). These two schemes are derived by approximating the global instantaneous information in the CMMSE combining and the local instantaneous information in the LMMSE combining with the global and local statistics information by asymptotic analysis and matrix expectation approximation, respectively. Moreover, by applying the low-complexity SSOR algorithm to iteratively solve the matrix inversion in the LMMSE combining, we derive three distributed SSOR-based LMMSE combining schemes, distinguished from the applied information and initial values.

Channel-Aware Conditional Diffusion Model for Secure MU-MISO Communications

While information securityis a fundamental requirement for wireless communications, conventional optimization based approaches often struggle with real-time implementation, and deep models, typically discriminative in nature, may lack the ability to cope with unforeseen scenarios. To address this challenge, this paper investigates the design of legitimate beamforming and artificial noise (AN) to achieve physical layer security by exploiting the conditional diffusion model. Specifically, we reformulate the security optimization as a conditional generative process, using a diffusion model to learn the inherent distribution of near-optimal joint beamforming and AN strategies. We employ a U-Net architecture with cross-attention to integrate channel state information, as the basis for the generative process. Moreover, we fine-tune the trained model using an objective incorporating the sum secrecy rate such that the security performance is further enhanced. Finally, simulation results validate the learning process convergence and demonstrate that the proposed generative method achieves superior secrecy performance across various scenarios as compared with the baselines.

ShardMemo: Masked MoE Routing for Sharded Agentic LLM Memory

Agentic large language model (LLM) systems rely on external memory for long-horizon state and concurrent multi-agent execution, but centralized indexes and heuristic partitions become bottlenecks as memory volume and parallel access grow. We present ShardMemo, a budgeted tiered memory service with Tier A per-agent working state, Tier B sharded evidence with shard-local approximate nearest neighbor (ANN) indexes, and Tier C, a versioned skill library. Tier B enforces scope-before-routing: structured eligibility constraints mask ineligible shards before routing or ANN search. We cast shard probing as masked mixture-of-experts (MoE) routing over eligible shards, probing up to $B_{\mathrm{probe}}$ shards via Top-$B_{\mathrm{probe}}$ or adaptive Top-$P$, and use cost-aware gating over profile/observation/session shard families; the router is trained from evidence-to-shard supervision. On LoCoMo, ShardMemo improves over the strongest baseline (GAM) by +5.11 to +6.82 F1 across question categories. Under a fixed-budget routing setting ($B_{\mathrm{probe}}=3$), ShardMemo improves over cosine-to-prototype shard routing by +6.87 F1 while reducing retrieval work (VecScan 521->414, -20.5%) and p95 latency (95->76 ms). On long-context HotpotQA, ShardMemo achieves 63.41/61.88/57.95 F1 at 56K/224K/448K tokens. On ToolBench, Tier C reaches 0.97 Precision@3 and 1.94 StepRed (+10.2% and +7.2% over embedding-similarity retrieval).

Semantic-Aware Command and Control Transmission for Multi-UAVs

Uncrewed aerial vehicles (UAVs) have played an important role in the low-altitude economy and have been used in various applications. However, with the increasing number of UAVs and explosive wireless data, the existing bit-oriented communication network has approached the Shannon capacity, which cannot satisfy the quality of service (QoS) with ultra-reliable low-latency communication (URLLC) requirements for command and control (C\&C) transmission in bit-oriented UAV communication networks. To address this issue, we propose a novel semantic-aware C\&C transmission for multi-UAVs under limited wireless resources. Specifically, we leverage semantic similarity to measure the variation in C\&C messages for each UAV over continuous transmission time intervals (TTIs) and capture the correlation of C\&C messages among UAVs, enabling multicast transmission. Based on the semantic similarity and the importance of UAV commands, we design a trigger function to quantify the QoS of UAVs. Then, to maximize the long-term QoS and exploit multicast opportunities of C\&C messages induced by semantic similarity, we develop a proximal policy optimization (PPO) algorithm to jointly determine the transmission mode (unicast/multicast/idle) and the allocation of limited resource blocks (RBs) between a base station (BS) and UAVs. Experimental results show that our proposed semantic-aware framework significantly increases transmission efficiency and improves effectiveness compared with bit-oriented UAV transmission.

SKANet: A Cognitive Dual-Stream Framework with Adaptive Modality Fusion for Robust Compound GNSS Interference Classification

As the electromagnetic environment becomes increasingly complex, Global Navigation Satellite Systems (GNSS) face growing threats from sophisticated jamming interference. Although Deep Learning (DL) effectively identifies basic interference, classifying compound interference remains difficult due to the superposition of diverse jamming sources. Existing single-domain approaches often suffer from performance degradation because transient burst signals and continuous global signals require conflicting feature extraction scales. We propose the Selective Kernel and Asymmetric convolution Network(SKANet), a cognitive deep learning framework built upon a dual-stream architecture that integrates Time-Frequency Images (TFIs) and Power Spectral Density (PSD). Distinct from conventional fusion methods that rely on static receptive fields, the proposed architecture incorporates a Multi-Branch Selective Kernel (SK) module combined with Asymmetric Convolution Blocks (ACBs). This mechanism enables the network to dynamically adjust its receptive fields, acting as an adaptive filter that simultaneously captures micro-scale transient features and macro-scale spectral trends within entangled compound signals. To complement this spatial-temporal adaptation, a Squeeze-and-Excitation (SE) mechanism is integrated at the fusion stage to adaptively recalibrate the contribution of heterogeneous features from each modality. Evaluations on a dataset of 405,000 samples demonstrate that SKANet achieves an overall accuracy of 96.99\%, exhibiting superior robustness for compound jamming classification, particularly under low Jamming-to-Noise Ratio (JNR) regimes.

PhyG-MoE: A Physics-Guided Mixture-of-Experts Framework for Energy-Efficient GNSS Interference Recognition

Complex electromagnetic interference increasingly compromises Global Navigation Satellite Systems (GNSS), threatening the reliability of Space-Air-Ground Integrated Networks (SAGIN). Although deep learning has advanced interference recognition, current static models suffer from a \textbf{fundamental limitation}: they impose a fixed computational topology regardless of the input's physical entropy. This rigidity leads to severe resource mismatch, where simple primitives consume the same processing cost as chaotic, saturated mixtures. To resolve this, this paper introduces PhyG-MoE (Physics-Guided Mixture-of-Experts), a framework designed to \textbf{dynamically align model capacity with signal complexity}. Unlike static architectures, the proposed system employs a spectrum-based gating mechanism that routes signals based on their spectral feature entanglement. A high-capacity TransNeXt expert is activated on-demand to disentangle complex features in saturated scenarios, while lightweight experts handle fundamental signals to minimize latency. Evaluations on 21 jamming categories demonstrate that PhyG-MoE achieves an overall accuracy of 97.58\%. By resolving the intrinsic conflict between static computing and dynamic electromagnetic environments, the proposed framework significantly reduces computational overhead without performance degradation, offering a viable solution for resource-constrained cognitive receivers.

LiQSS: Post-Transformer Linear Quantum-Inspired State-Space Tensor Networks for Real-Time 6G

Proactive and agentic control in Sixth-Generation (6G) Open Radio Access Networks (O-RAN) requires control-grade prediction under stringent Near-Real-Time (Near-RT) latency and computational constraints. While Transformer-based models are effective for sequence modeling, their quadratic complexity limits scalability in Near-RT RAN Intelligent Controller (RIC) analytics. This paper investigates a post-Transformer design paradigm for efficient radio telemetry forecasting. We propose a quantum-inspired many-body state-space tensor network that replaces self-attention with stable structured state-space dynamics kernels, enabling linear-time sequence modeling. Tensor-network factorizations in the form of Tensor Train (TT) / Matrix Product State (MPS) representations are employed to reduce parameterization and data movement in both input projections and prediction heads, while lightweight channel gating and mixing layers capture non-stationary cross-Key Performance Indicator (KPI) dependencies. The proposed model is instantiated as an agentic perceive-predict xApp and evaluated on a bespoke O-RAN KPI time-series dataset comprising 59,441 sliding windows across 13 KPIs, using Reference Signal Received Power (RSRP) forecasting as a representative use case. Our proposed Linear Quantum-Inspired State-Space (LiQSS) model is 10.8x-15.8x smaller and approximately 1.4x faster than prior structured state-space baselines. Relative to Transformer-based models, LiQSS achieves up to a 155x reduction in parameter count and up to 2.74x faster inference, without sacrificing forecasting accuracy.

Effective outdoor pathloss prediction: A multi-layer segmentation approach with weighting map

Predicting pathloss by considering the physical environment is crucial for effective wireless network planning. Traditional methods, such as ray tracing and model-based approaches, often face challenges due to high computational complexity and discrepancies between models and real-world environments. In contrast, deep learning has emerged as a promising alternative, offering accurate path loss predictions with reduced computational complexity. In our research, we introduce a ResNet-based model designed to enhance path loss prediction. We employ innovative techniques to capture key features of the environment by generating transmission (Tx) and reception (Rx) depth maps, as well as a distance map from the geographic data. Recognizing the significant attenuation caused by signal reflection and diffraction, particularly at high frequencies, we have developed a weighting map that emphasizes the areas adjacent to the direct path between Tx and Rx for path loss prediction. {Extensive simulations demonstrate that our model outperforms PPNet, RPNet, and Vision Transformer (ViT) by 1.2-3.0 dB using dataset of ITU challenge 2024 and ICASSP 2023. In addition, the floating point operations (FLOPs) of the proposed model is 60\% less than those of benchmarks.} Additionally, ablation studies confirm that the inclusion of the weighting map significantly enhances prediction performance.