arXiv subjects

Dongfang Xu

Publications and source records attributed to Dongfang Xu.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Framework for Characterizing General MIMO Channels

Modern MIMO systems are evolving toward higher-dimensional and more flexible architectures, such as distributed and holographic MIMO, offering substantial benefits while giving rise to increasingly complex channel correlation structures. This growing architectural diversity makes it difficult to characterize the fundamental limits of different MIMO systems on a case-by-case basis, motivating a unified analytical framework applicable across a broad range of architectures. This paper addresses this research gap by investigating a generally correlated Rayleigh channel whose vectorized form follows a general Gaussian distribution with an arbitrary covariance matrix. For that purpose, we first prove that the spectral norm of the channel matrix is bounded in the asymptotic regime where the numbers of transmit and receive antennas grow proportionally. We then derive a deterministic approximation for the ergodic mutual information, with an explicit convergence rate governed by the structure of the channel correlation. The approximation is characterized by a pair of matrix-valued self-consistent equations, for which we establish the existence and uniqueness of the solution and propose an iterative numerical algorithm. Furthermore, we develop a framework based on positive linear maps to analyze the stability of these equations, which can facilitate the spectral analysis of broader classes of random matrices. The proposed characterization unifies many existing results for structured MIMO channels as special cases while remaining applicable to a broad class of general MIMO architectures that are difficult to evaluate using existing analytical frameworks. To demonstrate its utility, we apply the developed theory to two representative systems, namely downlink distributed MIMO and uplink heterogeneous MIMO. Numerical results confirm the accuracy of the derived deterministic approximations.

cs.IT↗

arXiv2026

RF-Agent: Hierarchical Language-Agent Control for Instruction-Conditioned Active Spectrum Sensing

Active radio-frequency (RF) sensing must acquire evidence under receiver limits while following confirmation, recovery, and stopping instructions. \newhl{We propose RF-Agent, a closed-loop architecture combining language supervision, episode memory, deterministic RF execution, perception feedback, and evidence-based reporting.} An independent auditor checks trajectory compliance. We derive acquisition and supervisory-request bounds, characterize full-history token complexity, and bound joint success by output validity and evidence capacity. \newhl{ActiveRF-AD tests instruction changes at fixed states and evaluates joint success, requiring compliance and RF correctness in the same episode.} \newhl{Training on different instructions at shared sensing states raises counterfactual-pair accuracy from 24.03\% to 96.22\% and Core joint success from 65.13\% to 72.12\%. Of the 6.99-point joint-success gain, 6.73 points reflect a decrease in the fraction of all episodes that are RF-correct but noncompliant.} \newhl{At Core budget three, paired-training hierarchical control achieves 66.60\% joint success versus 9.17\% for direct-action control.} \newhl{In a separate comparison at the same budget, RF-Agent improves joint success by 2.31 points and reduces RF acquisitions by 12.3\% relative to an initial-state planner, at increased inference cost.} Cross-backbone diagnostics cover three model families. These results show how instruction-responsive control improves task completion beyond what RF accuracy alone reveals.

eess.SP↗

arXiv2026

Movable-Antenna-Enhanced ISAC: Optimal Antenna Trajectory and Beamforming Design

Integrated sensing and communication (ISAC) is a key enabling technology for next-generation wireless networks. However, most existing ISAC systems rely on fixed-position antennas, which restrict performance when balancing sensing and communication objectives. Movable antenna (MA) technology introduces additional spatial degrees of freedom through antenna mobility, yet existing studies on MA-enabled ISAC schemes mainly consider static antenna repositioning and fail to fully exploit this capability. By leveraging spatio-temporal sampling enabled by antenna motion, optimized MA trajectories can synthesize large virtual aperture arrays, thereby improving angular resolution and reducing sensing ambiguity. To this end, this paper investigates a dynamic MA-enabled ISAC system and studies the joint design of MA trajectories and transmit beamforming. We formulate a joint trajectory and beamforming optimization problem to minimize sensing beampattern mismatch under communication quality-of-service constraints. A branch-and-bound-based algorithm is developed to obtain the globally optimal solution. Numerical results show that the proposed framework significantly outperforms baseline schemes with only one or two antenna repositioning steps, demonstrating its practical feasibility.

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arXiv2026

Communication-Efficient Multi-Modal Edge Inference via Uncertainty-Aware Distributed Learning

Semantic communication is emerging as a key enabler for distributed edge intelligence due to its capability to convey task-relevant meaning. However, achieving communication-efficient training and robust inference over wireless links remains challenging. This challenge is further exacerbated for multi-modal edge inference (MMEI) by two factors: 1) prohibitive communication overhead for distributed learning over bandwidth-limited wireless links, due to the \emph{multi-modal} nature of the system; and 2) limited robustness under varying channels and noisy multi-modal inputs. In this paper, we propose a three-stage communication-aware distributed learning framework to improve training and inference efficiency while maintaining robustness over wireless channels. In Stage~I, devices perform local multi-modal self-supervised learning to obtain shared and modality-specific encoders without device--server exchange, thereby reducing the communication cost. In Stage~II, distributed fine-tuning with centralized evidential fusion calibrates per-modality uncertainty and reliably aggregates features distorted by noise or channel fading. In Stage~III, an uncertainty-guided feedback mechanism selectively requests additional features for uncertain samples, optimizing the communication--accuracy tradeoff in the distributed setting. Experiments on RGB--depth indoor scene classification show that the proposed framework attains higher accuracy with far fewer training communication rounds and remains robust to modality degradation or channel variation, outperforming existing self-supervised and fully supervised baselines.

cs.LG↗

arXiv2025

Adaptive Sensing Performance Design for Enhancing Secure Communication in Networked ISAC Systems

The channel state information (CSI) of an eavesdropper is crucial for physical layer security (PLS) design, but it is difficult to obtain due to the passive and non-cooperative nature of the eavesdropper. To this end, integrated sensing and communication (ISAC) offers a novel solution by estimating the CSI of the eavesdropper based on sensing information. However, existing studies normally impose explicit and fixed sensing performance requirement without considering the varying communication conditions, which hinders the system from fully exploiting the synergy between sensing and communication. To address this issue, this paper proposes sensing-enhanced secure communication with adaptive sensing performance. Specifically, we formulate the sensing performance implicitly in the information leakage rate and adaptively optimize it for the minimization of the power consumption, offering enhanced flexibility and adaptability in sensing performance. We consider both centralized and decentralized designs to thoroughly investigate the impact of network structure on system performance and complexity. Specifically, we devise a block coordinate descent (BCD)-based method for centralized design. For decentralized design, we develop an optimization framework based on consensus alternating direction method of multipliers (ADMM) to reduce complexity and information exchange overhead. Experimental results demonstrate the advantage of the proposed implicit sensing performance requirement design due to its capability to adaptively adjust the sensing performance to enhance the system performance for varying system configurations.

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arXiv2025

Fluid Antenna Meets RIS: Random Matrix Analysis and Two-Timescale Design for Multi-User Communications

The reconfigurability of fluid antenna systems (FASs) and reconfigurable intelligent surfaces (RISs) provides significant flexibility in optimizing channel conditions by jointly adjusting the positions of fluid antennas and the phase shifts of RISs. However, it is challenging to acquire the instantaneous channel state information (CSI) for both fluid antennas and RISs, while frequent adjustment of antenna positions and phase shifts will significantly increase the system complexity. To tackle this issue, this paper investigates the two-timescale design for FAS-RIS multi-user systems with linear precoding, where only the linear precoder design requires instantaneous CSI of the end-to-end channel, while the FAS and RIS optimization relies on statistical CSI. The main challenge comes from the complex structure of channel and inverse operations in linear precoding, such as regularized zero-forcing (RZF) and zero-forcing (ZF). Leveraging on random matrix theory (RMT), we first investigate the fundamental limits of FAS-RIS systems with RZF/ZF precoding by deriving the ergodic sum rate (ESR). This result is utilized to determine the minimum number of selected antennas to achieve a given ESR. Based on the evaluation result, we propose an algorithm to jointly optimize the antenna selection, regularization factor of RZF, and phase shifts at the RIS. Numerical results validate the accuracy of performance evaluation and demonstrate that the performance gain brought by joint FAS and RIS design is more pronounced with a larger number of users.

cs.IT↗

arXiv2025

Globally Optimal Movable Antenna-Enhanced multiuser Communication: Discrete Antenna Positioning, Motion Power Consumption, and Imperfect CSI

Movable antennas (MAs) represent a promising paradigm to enhance the spatial degrees of freedom of conventional multi-antenna systems by dynamically adapting the positions of antenna elements within a designated transmit area. In particular, by employing electro-mechanical MA drivers, the positions of the MA elements can be adjusted to shape a favorable spatial correlation for improving system performance. Although preliminary research has explored beamforming designs for MA systems, the intricacies of the power consumption and the precise positioning of MA elements are not well understood. Moreover, the assumption of perfect CSI adopted in the literature is impractical due to the significant pilot overhead and the extensive time to acquire perfect CSI. To address these challenges, we model the motion of MA elements through discrete steps and quantify the associated power consumption as a function of these movements. Furthermore, by leveraging the properties of the MA channel model, we introduce a novel CSI error model tailored for MA systems that facilitates robust resource allocation design. In particular, we optimize the beamforming and the MA positions at the BS to minimize the total BS power consumption, encompassing both radiated and MA motion power while guaranteeing a minimum required SINR for each user. To this end, novel algorithms exploiting the branch and bound (BnB) method are developed to obtain the optimal solution for perfect and imperfect CSI. Moreover, to support practical implementation, we propose low-complexity algorithms with guaranteed convergence by leveraging successive convex approximation (SCA). Our numerical results validate the optimality of the proposed BnB-based algorithms. Furthermore, we unveil that both proposed SCA-based algorithms approach the optimal performance within a few iterations, thus highlighting their practical advantages.

eess.SP↗

arXiv2025

No Eigenvalues Outside the Limiting Support of Generally Correlated and Noncentral Sample Covariance Matrices

Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the ``no-eigenvalue'' property have been obtained for random matrices with different correlation structures. However, the related spectral analysis for generally correlated and noncentral random matrices is still incomplete, and this paper aims to fill this research gap. Specifically, we consider matrices whose columns are independent but with non-zero means and non-identical correlations. Under high-dimensional asymptotics where both the number of rows and columns grow simultaneously to infinity, we first establish the almost sure convergence of the ESD for the concerned random matrices to a deterministic limit, assuming mild conditions. Furthermore, we prove that with probability 1, no eigenvalues will appear in any closed interval outside the support of the limiting distribution for matrices with sufficiently large dimensions. The above results can be applied to different areas such as statistics, wireless communications, and signal processing. In this paper, we apply the derived results to two communication scenarios: 1) We determine the limiting performance of the signal-to-interference-plus-noise ratio for multi-user multiple-input multiple-output (MIMO) systems with linear minimum mean-square error receivers; and 2) We establish the invertibility of zero-forcing precoding matrices in downlink MIMO systems, providing theoretical guarantees.

math.ST↗

arXiv2025

Joint Radiation Power, Antenna Position, and Beamforming Optimization for Pinching-Antenna Systems with Motion Power Consumption

Pinching-antenna systems (PASS) have been recently proposed to improve the performance of wireless networks by reconfiguring both the large-scale and small-scale channel conditions. However, existing studies ignore the physical constraints of antenna placement and assume fixed antenna radiation power. To fill this research gap, this paper investigates the design of PASS taking into account the motion power consumption of pinching-antennas (PAs) and the impact of adjustable antenna radiation power. To that end, we minimize the average power consumption for a given quality-of-service (QoS) requirement, by jointly optimizing the antenna positions, antenna radiation power ratios, and transmit beamforming. To the best of the authors' knowledge, this is the first work to consider radiation power optimization in PASS, which provides an additional degree of freedom (DoF) for system design. The cases with both continuous and discrete antenna placement are considered, where the main challenge lies in the fact that the antenna positions affect both the magnitude and phase of the channel coefficients of PASS, making system optimization very challenging. To tackle the resulting unique obstacles, an alternating direction method of multipliers (ADMM)-based framework is proposed to solve the problem for continuous antenna movement, while its discrete counterpart is formulated as a mixed integer nonlinear programming (MINLP) problem and solved by the block coordinate descent (BCD) method. Simulation results validate the performance enhancement achieved by incorporating PA movement power assumption and adjustable radiation power into PASS design, while also demonstrating the efficiency of the proposed optimization framework. The benefits of PASS over conventional multiple-input multiple-output (MIMO) systems in mitigating the large-scale path loss and inter-user interference is also revealed.

eess.SP↗

arXiv2025

Multi-Modal Self-Supervised Semantic Communication

Semantic communication is emerging as a promising paradigm that focuses on the extraction and transmission of semantic meanings using deep learning techniques. While current research primarily addresses the reduction of semantic communication overhead, it often overlooks the training phase, which can incur significant communication costs in dynamic wireless environments. To address this challenge, we propose a multi-modal semantic communication system that leverages multi-modal self-supervised learning to enhance task-agnostic feature extraction. The proposed approach employs self-supervised learning during the pre-training phase to extract task-agnostic semantic features, followed by supervised fine-tuning for downstream tasks. This dual-phase strategy effectively captures both modality-invariant and modality-specific features while minimizing training-related communication overhead. Experimental results on the NYU Depth V2 dataset demonstrate that the proposed method significantly reduces training-related communication overhead while maintaining or exceeding the performance of existing supervised learning approaches. The findings underscore the advantages of multi-modal self-supervised learning in semantic communication, paving the way for more efficient and scalable edge inference systems.

cs.CV↗

arXiv2025

Decentralized MIMO Systems with Imperfect CSI using LMMSE Receivers

Centralized baseband processing (CBP) is required to achieve the full potential of massive multiple-input multiple-output (MIMO) systems. However, due to the large number of antennas, CBP suffers from two major issues: 1) Tremendous data interconnection between radio frequency (RF) circuitry and processing fabrics; and 2) high-dimensional computation. To this end, decentralized baseband processing (DBP) has been proposed, where the antennas at the BS are partitioned into clusters connected to separate RF circuits and equipped with separate computing units. Unfortunately, due to the decentralized structure, the optimal fusion scheme and performance analysis for DBP with general spatial correlation between clusters and imperfect channel state information (CSI) are not available in the literature. In this paper, we consider a decentralized MIMO system where all clusters adopt linear minimum mean-square error (LMMSE) receivers with imperfect CSI. Specifically, we first establish the optimal linear fusion scheme which has high computational and data input/output (I/O) costs. To reduce the costs, we further propose two sub-optimal fusion schemes with reduced complexity. For all three schemes, we derive the closed-form expressions for the signal-to-interference-and-noise ratio (SINR) by leveraging random matrix theory (RMT) and demonstrate the conditions under which the sub optimal schemes are optimal. Furthermore, we determine the optimal regularization parameter for decentralized LMMSE receivers, identify the best antenna partitioning strategy, and prove that the SINR will decrease as the number of clusters increases. Numerical simulations validate the accuracy of the theoretical results.

cs.IT↗

arXiv2024

Sensing-assisted Robust SWIPT for Mobile Energy Harvesting Receivers in Networked ISAC Systems

Simultaneous wireless information and power transfer (SWIPT) has been proposed to offer communication services and transfer power to the energy harvesting receiver (EHR) concurrently. However, existing works mainly focused on static EHRs, without considering the location uncertainty caused by the movement of EHRs and location estimation errors. To tackle this issue, this paper considers the sensing-assisted SWIPT design in a networked integrated sensing and communication (ISAC) system in the presence of location uncertainty. A two-phase robust design is proposed to reduce the location uncertainty and improve the power transfer efficiency. In particular, each time frame is divided into two phases, i.e., sensing and WPT phases, via time-splitting. The sensing phase performs collaborative sensing to localize the EHR, whose results are then utilized in the WPT phase for efficient WPT. To minimize the power consumption with given communication and power transfer requirements, a two-layer optimization framework is proposed to jointly optimize the time-splitting ratio, coordinated beamforming policy, and sensing node selection. Simulation results validate the effectiveness of the proposed design and demonstrate the existence of an optimal time-splitting ratio for given location uncertainty.

eess.SP↗

arXiv2024

Efficient UAV Hovering, Resource Allocation, and Trajectory Design for ISAC with Limited Backhaul Capacity

In this paper, we investigate the joint resource allocation and trajectory design for a multi-user, multi-target unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) system, where the link capacity between a ground base station (BS) and the UAV is limited. The UAV conducts target sensing and information transmission in orthogonal time slots to prevent interference. As is common in practical systems, sensing is performed while the UAV hovers, allowing the UAV to acquire high-quality sensing data. Subsequently, the acquired sensing data is offloaded to the ground BS for further processing. We jointly optimize the UAV trajectory, UAV velocity, beamforming for the communication users, power allocated to the sensing beam, and time of hovering for sensing to minimize the power consumption of the UAV while ensuring the communication quality of service (QoS) and successful sensing. Due to the prohibitively high complexity of the resulting non-convex mixed integer non-linear program (MINLP), we employ a series of transformations and optimization techniques, including semidefinite relaxation, big-M method, penalty approach, and successive convex approximation, to obtain a low-complexity suboptimal solution. Our simulation results reveal that 1) the proposed design achieves significant power savings compared to two baseline schemes; 2) stricter sensing requirements lead to longer sensing times, highlighting the challenge of efficiently managing both sensing accuracy and sensing time; 3) the optimized trajectory design ensures precise hovering directly above the targets during sensing, enhancing sensing quality and enabling the application of energy-focused beams; and 4) the proposed trajectory design balances the capacity of the backhaul link and the downlink rate of the communication users.

eess.SP↗

arXiv2024

Sensing-aided Near-Field Secure Communications with Mobile Eavesdroppers

The additional degree of freedom (DoF) in the distance domain of near-field communication offers new opportunities for physical layer security (PLS) design. However, existing works mainly consider static eavesdroppers, and the related study with mobile eavesdroppers is still in its infancy due to the difficulty in obtaining the channel state information (CSI) of the eavesdropper. To this end, we propose to leverage the sensing capability of integrated sensing and communication (ISAC) systems to assist PLS design. To comprehensively study the dynamic behaviors of the system, we propose a Pareto optimization framework, where a multi-objective optimization problem (MOOP) is formulated to simultaneously optimize three key performance metrics: power consumption, number of securely served users, and tracking performance, while guaranteeing the achievable rate of the users with a given leakage rate constraint. A globally optimal design based on the generalized Benders decomposition (GBD) method is proposed to achieve the Pareto optimal solutions. To reduce the computational complexity, we further design a low-complexity algorithm based on zero-forcing (ZF) beamforming and successive convex approximation (SCA). Simulation results validate the effectiveness of the proposed algorithms and reveal the intrinsic trade-offs between the three performance metrics. It is observed that near-field communication offers a favorable beam diffraction effect for PLS, where the energy of the information signal is nulled around the eavesdropper and focused on the users.

eess.SP↗

arXiv2024

Resource Allocation Design for Next-Generation Multiple Access: A Tutorial Overview

Multiple access is the cornerstone technology for each generation of wireless cellular networks and resource allocation design plays a crucial role in multiple access. In this paper, we present a comprehensive tutorial overview for junior researchers in this field, aiming to offer a foundational guide for resource allocation design in the context of next-generation multiple access (NGMA). Initially, we identify three types of channels in future wireless cellular networks over which NGMA will be implemented, namely: natural channels, reconfigurable channels, and functional channels. Natural channels are traditional uplink and downlink communication channels; reconfigurable channels are defined as channels that can be proactively reshaped via emerging platforms or techniques, such as intelligent reflecting surface (IRS), unmanned aerial vehicle (UAV), and movable/fluid antenna (M/FA); and functional channels support not only communication but also other functionalities simultaneously, with typical examples including integrated sensing and communication (ISAC) and joint computing and communication (JCAC) channels. Then, we introduce NGMA models applicable to these three types of channels that cover most of the practical communication scenarios of future wireless communications. Subsequently, we articulate the key optimization technical challenges inherent in the resource allocation design for NGMA, categorizing them into rate-oriented, power-oriented, and reliability-oriented resource allocation designs. The corresponding optimization approaches for solving the formulated resource allocation design problems are then presented. Finally, simulation results are presented and discussed to elucidate the practical implications and insights derived from resource allocation designs in NGMA.

cs.IT↗

arXiv2024

Wireless Information and Energy Transfer in the Era of 6G Communications

Wireless information and energy transfer (WIET) represents an emerging paradigm which employs controllable transmission of radio-frequency signals for the dual purpose of data communication and wireless charging. As such, WIET is widely regarded as an enabler of envisioned 6G use cases that rely on energy-sustainable Internet-of-Things (IoT) networks, such as smart cities and smart grids. Meeting the quality-of-service demands of WIET, in terms of both data transfer and power delivery, requires effective co-design of the information and energy signals. In this article, we present the main principles and design aspects of WIET, focusing on its integration in 6G networks. First, we discuss how conventional communication notions such as resource allocation and waveform design need to be revisited in the context of WIET. Next, we consider various candidate 6G technologies that can boost WIET efficiency, namely, holographic multiple-input multiple-output, near-field beamforming, terahertz communication, intelligent reflecting surfaces (IRSs), and reconfigurable (fluid) antenna arrays. We introduce respective WIET design methods, analyze the promising performance gains of these WIET systems, and discuss challenges, open issues, and future research directions. Finally, a near-field energy beamforming scheme and a power-based IRS beamforming algorithm are experimentally validated using a wireless energy transfer testbed. The vision of WIET in communication systems has been gaining momentum in recent years, with constant progress with respect to theoretical but also practical aspects. The comprehensive overview of the state of the art of WIET presented in this paper highlights the potentials of WIET systems as well as their overall benefits in 6G networks.

cs.IT↗

arXiv2024

Globally Optimal Resource Allocation Design for Discrete Phase Shift IRS-Assisted Multiuser Networks with Perfect and Imperfect CSI

Intelligent reflecting surfaces (IRSs) are a promising low-cost solution for achieving high spectral and energy efficiency in future communication systems by enabling the customization of wireless propagation environments. Despite the plethora of research on resource allocation design for IRS-assisted multiuser wireless communication systems, the optimal design and the corresponding performance upper bound are still not fully understood. To bridge this gap in knowledge, in this paper, we investigate the optimal resource allocation design for IRS-assisted multiuser multiple-input single-output systems employing practical discrete IRS phase shifters. In particular, we jointly optimize the beamforming vector at the base station and the discrete IRS phase shifts to minimize the total transmit power for the cases of perfect and imperfect channel state information (CSI) knowledge. To this end, two novel algorithms based on the generalized Benders decomposition (GBD) method are developed to obtain the globally optimal solution for perfect and imperfect CSI, respectively. Moreover, to facilitate practical implementation, we propose two corresponding low-complexity suboptimal algorithms with guaranteed convergence by capitalizing on successive convex approximation (SCA). In particular, for imperfect CSI, we adopt a bounded error model to characterize the CSI uncertainty and propose a new transformation to convexify the robust quality-of-service constraints. Our numerical results confirm the optimality of the proposed GBD-based algorithms for the considered system for both perfect and imperfect CSI. Furthermore, we unveil that both proposed SCA-based algorithms can attain a locally optimal solution within a few iterations. Moreover, compared with the state-of-the-art solution based on alternating optimization, the proposed low-complexity SCA-based schemes achieve a significant performance gain.

cs.IT↗

arXiv2024

Fundamental Limits of Optical Fiber MIMO Channels With Finite Blocklength

The multiple-input and multiple-output (MIMO) technique is regarded as a promising approach to boost the throughput and reliability of optical fiber communications. However, the fundamental limits of optical fiber MIMO systems with finite block-length (FBL) are not available in the literature. This paper studies the fundamental limits of optical fiber multicore/multimode systems in the FBL regime when the coding rate is a perturbation within $\mathcal{O}(\frac{1}{\sqrt{ML}})$ of the capacity, where M and L represent the number of transmit channels and blocklength, respectively. Considering the Jacobi MIMO channel, which was proposed to model the nearly lossless propagation and the crosstalks in optical fiber systems, we derive the upper and lower bounds for the optimal error probability. For that purpose, we first set up the central limit theorem for the information density in the asymptotic regime where the number of transmit, receive, available channels and the blocklength go to infinity at the same pace. The result is then utilized to derive the upper and lower bounds for the optimal average error probability with the concerned rate. The derived theoretical results reveal interesting physical insights for Jacobi MIMO channels with FBL. First, the derived bounds for Jacobi channels degenerate to those for Rayleigh channels when the number of available channels approaches infinity. Second, the high signal-to-noise (SNR) approximation indicates that a larger number of available channels results in a larger error probability. Numerical results validate the accuracy of the theoretical results and show that the derived bounds are closer to the performance of practical LDPC codes than outage probability.

cs.IT↗