Clustered cell-free networking is a promising paradigm for future mobile communication systems, which dynamically partitions the whole network into multiple small subnetworks to avoid the cell-edge problem in cellular networks. To optimize network partition, previous approaches primarily relied on heuristics and relaxation techniques. Recent studies leveraged graph partitioning theory to address this problem by representing the wireless network as an undirected bipartite graph. In this paper, we focus on the load balanced clustered cell-free networking problem with the objective of maximizing the minimum sum rate among all subnetworks. In contrast to previous works, we propose a new directed graph model and equivalently transform the problem into a sequence of min-max K-cut problems. Subsequently, a streaming balanced assignment algorithm is proposed to solve min-max K-cut problems. Building upon this, we develop a sequential min-max K-cut approach with theoretical guarantees. Simulation results demonstrate that our method outperforms existing algorithms by significantly improving the minimum subnetwork sum rate, thereby effectively balancing the loads of subnetworks.

Sparse superposition (SS) codes provide an efficient communication scheme over the Gaussian channel, utilizing the vector approximate message passing (VAMP) decoder for rotational invariant design matrices [1]. Previous work has established that the VAMP decoder for SS achieves Shannon capacity when the design matrix satisfies a specific spectral criterion and exponential decay power allocation is used [2]. In this work, we propose a spatially coupled VAMP (SC-VAMP) decoder for SS with spatially coupled design matrices. Based on state evolution (SE) analysis, we demonstrate that the SC-VAMP decoder is capacity-achieving when the design matrices satisfy the spectra criterion. Empirically, we show that the SC-VAMP decoder outperforms the VAMP decoder with exponential decay power allocation, achieving a lower section error rate. All codes are available on https://github.com/yztfu/SC-VAMP-for-Superposition-Code.git.

We investigate the performance of a Bayesian statistician tasked with recovering a rank-k signal matrix SS⊤∈ ℝn×n, corrupted by element-wise additive Gaussian noise. This problem lies at the core of numerous applications in machine learning, signal processing, and statistics. We derive an analytic expression for the asymptotic mean-square error (MSE) of the Bayesian estimator under mismatches in the assumed signal rank, signal power, and signal-to-noise ratio (SNR), considering both sphere and Gaussian signals. Additionally, we conduct a rigorous analysis of how rank mismatch influences the asymptotic MSE. Our primary technical tools include the spectrum of Gaussian orthogonal ensembles (GOE) with low-rank perturbations and asymptotic behavior of k-dimensional spherical integrals.

Clustered cell-free networking that dynamically decomposes a network into multiple subnetworks is emerging as a promising solution to the cell-edge problem in mobile communication systems. Maximizing the minimum subnetwork sum ergodic capacity is of great importance for balancing the loads of different subnetworks. Such a load-balanced clustered cell-free networking problem was proposed recently, yet still lacks efficient algorithms due to its complicated objective function and combinatorial nature. Recognizing these challenges, this paper proposes a tight relaxation method to equivalently transform the original problem into a continuous one that shares the same optimal solution. The relaxed problem is a nonconvex-linear minmax problem, which can be solved by finding its Nash equilibrium. We then propose an alternating gradient projection (AGP) algorithm to effectively tackle it, with a guaranteed convergence. Simulation results show that our approach significantly outperforms the existing benchmarks.

This paper presents a novel sequential max k-cut approach to the pilot assignment problem in cell-free networks. In contrast to the existing max k-cut formulations that were proposed based on intuitions or qualitative analyses, we first establish a theoretical connection between pilot assignment and max k-cut, which avoids the performance degradation brought by the inaccurate max k-cut formulation. Specifically, we employ optimization techniques to equivalently transform the pilot assignment problem for uplink throughput maximization into a series of max k-cut problems with updated weights, leading to a sequential max k-cut approach. Moreover, different from the existing works that decouple pilot assignment and power control, this approach enables us to jointly optimize pilot assignment and power control with a customized scheme developed for further improvement of overall throughput and user fairness. Simulation results show the effectiveness and efficiency of the proposed approach, exhibiting significant improvement over existing methods. This sequential max k-cut approach could serve as a promising candidate for mitigating the performance deterioration resulting from severe pilot reuse in future ultra-dense cell-free networks.

Determining the network capacity, which is a crucial performance metric of wireless systems, is becoming increasingly important with the growing need for future ultra-dense networks. There have been a multitude of works applying random matrix theory (RMT) to capacity analysis. However, most of them approximate the interference as noise and rely on the selection of hyper-parameters, and thus impairs the accuracy. In this paper, we first propose a double splitting model to decompose the capacity into four parts, two of which can be analytically calculated, while the other two are significantly smaller and thus have minimal impact on the overall accuracy. This helps to avoid the approximations of previous methods, simplifying the calculation of capacity and improving the numerical stability. Second, to compute the aforementioned smaller parts, we generalize the moment passing method to more scenarios, and avoid the hyper-parameter selection that impairs the robustness. We also derive the recursive expressions of the moments of any order, enabling flexible trade-offs between efficiency and accuracy. Numerical experiments demonstrate the high efficiency and accuracy of our methods.

Clustered cell-free networking is a promising networking scheme for future mobile communications systems where the base-stations (BSs) are densely deployed. Despite its great importance, finding the optimal networking strategy aiming at maximizing the sum rate of users in the network is a non-convex combinatorial optimization problem. Previous work relaxed the clustered cell-free networking problem into a graph min$K$-cut problem to solve it suboptimally. In this paper, we leverage optimization techniques to equivalently transform the original problem into a series of graph min$K$-cut problems with theoretical guarantee. It is worth mentioning that our approach is highly general, as it is applicable to various constraints, offering adaptability and flexibility to diverse practical networking scenarios. We apply this approach to three typical clustered cellfree networking problems. Simulation results show a consistent improvement of our approach compared to existing algorithms.

The sixth generation (6G) era is envisioned to be a fully intelligent and autonomous era, with physical and digital lifestyles merged together. Future wireless network architectures should provide a solid support for such new lifestyles. A key problem thus arises that what kind of network architectures are suitable for 6G. In this paper, we propose a capacity-guaranteed network (CGN) architecture, which provides high capacity for wireless devices densely distributed everywhere, and ensures a superior scalability with low signaling overhead and computation complexity simultaneously. Our theorem proves that the essence of a CGN architecture is to decompose the whole network into non-overlapping clusters with equal cluster sum capacity. Simulation results reveal that in terms of the minimum cluster sum capacity, the proposed CGN can achieve at least 30% performance gain compared with existing base station clustering (BS-clustering) architectures. In addition, our theorem is sufficiently general and can be applied for networks with different distributions of BSs and users.