OOIR: Observatory of International Research

Papers

(The median citation count of IEEE Transactions on Wireless Communications is 5. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-09-01 to 2025-09-01.)

Article	Citations
IEEE Communications Society	558
Energy-Efficient Edge Learning via Joint Data Deepening-and-Prefetching	279
Robust Symbol Level Precoding for Overlay Cognitive Radio Networks	278
Geometric View on Integrated Cascaded Channel of IRS-Aided Communications	271
Data-Driven Online Resource Allocation for User Experience Improvement in Mobile Edge Clouds	236
Channel Characterization for the 90 GHz Band in Aviation Environments	226
Adaptive Irregular Constellations for Full-Duplex Relaying With Residual Self-Interference	220
Bit-Metric Decoding Rate in Multi-User MIMO Systems: Applications	207
Sparse Code Multiple Access With Enhanced K-Repetition Scheme: Analysis and Design	197
Quadratic Displacement Operators—Theory and Application to Millimeter-Wave Channel Tracking	192
Density Evolution Analysis of the Iterative Joint Ordered-Statistics Decoding for NOMA	190
BanditLinQ: A Scalable Link Scheduling for Dense D2D Networks With One-Bit Feedback	181
Full-Duplex Cooperative Rate-Splitting for Multigroup Multicast With SWIPT	180
Analysis and Optimization of Cache-Enabled mmWave HetNets With Integrated Access and Backhaul	170
Joint Scattering Environment Sensing and Channel Estimation Based on Non-Stationary Markov Random Field	169
Joint Detection and Communication System Design via Combination of Index and Phase Modulations	168
Signal Domain Multicomponent-Based Secure Hybrid Precoding for mmWave Systems	166
Seeing the Unseen: The REVEAL Protocol to Expose the Wireless Man-in-the-Middle	160
Table of Contents	159
Resource-Aware Hierarchical Federated Learning in Wireless Video Caching Networks	159
IEEE Transactions on Wireless Communications Society Information	157
Memory AMP for Generalized MIMO: Coding Principle and Information-Theoretic Optimality	156
On the Statistical Channel Distribution and Effective Capacity Analysis of STAR-RIS-Assisted BAC-NOMA Systems	154
Joint User-Side Recommendation and D2D-Assisted Offloading for Cache-Enabled Cellular Networks With Mobility Consideration	153
Adaptive Compressive Spectrum Sensing Using a Deterministic Estimation Model for Wideband Cognitive Radios	152

Index Modulation With Circularly-Shifted Chirps for Dual-Function Radar and Communications	152
Optimal and Constrained RIS Profile Design for User Localization in OFDM Systems	150
RadiOrchestra: Proactive Management of Millimeter-Wave Self-Backhauled Small Cells via Joint Optimization of Beamforming, User Association, Rate Selection, and Admission Control	148
Convergence of Federated Learning Over a Noisy Downlink	147
On the Maximum Energy Efficiency of Random Access-Based OMA and NOMA in Multirate Environment	147
Joint Design of Equalization and Beamforming for Single-Carrier MIMO Transmission Over Millimeter-Wave and Sub-Terahertz Channels	145
Waveform Design for High-Order QAM Faster-Than-Nyquist Transmission in the Presence of Phase Noise	145
Communication-Efficient Personalized Federated Edge Learning for Massive MIMO CSI Feedback	145
Age of Information-Oriented Link Scheduling in Device-to-Device Networks	142
Ambient LoRa Backscatter System With Chirp Interval Modulation	141
Robust Group Target Awareness Inference in Multi-UAV-Enabled ISCC Networks Based on Split Deep Reinforcement Learning	140
Coverage and Capacity of Terahertz Cellular Networks With Joint Transmission	139
Dynamic Delay-Doppler-Angle Domain Channel Tracking for THz Massive MIMO-OTFS Communication Systems	137
Faster-Than-Nyquist Signaling for MIMO Communications	136
Ergodic Achievable Rate Analysis and Optimization of RIS-Assisted Millimeter-Wave MIMO Communication Systems	134
Graph Learning-Based Cooperative Spectrum Sensing With Corrupted RSSs in Spectrum-Heterogeneous Cognitive Radio Networks	134
Distributed Coordinated Precoding for MIMO Cellular Network Virtualization	134
On the Design and Performance of QRD-Based Beamforming Feedback for Wi-Fi Sensing	133
Secrecy Wireless Information and Power Transfer in Ultra-Dense Cloud Radio Access Networks	132
GNN-Assisted BiG-AMP: Joint Channel Estimation and Data Detection for Massive MIMO Receiver	130
Embedding Model-Based Fast Meta Learning for Downlink Beamforming Adaptation	130
Beyond Diagonal Reconfigurable Intelligent Surfaces in Wideband OFDM Communications: Circuit-Based Modeling and Optimization	128
Dual-Sided Active-IOS-Enhanced Secure Multi-Cell Systems Exploiting Eavesdroppers’ Statistical CSI	128
Collaborative Multi-Agent Deep Reinforcement Learning for Energy-Efficient Resource Allocation in Heterogeneous Mobile Edge Computing Networks	128
Scenario-Adaptive Meta-Learning for mmWave Beam Alignment	127
FDD Massive MIMO Channel Training: Optimal Rate-Distortion Bounds and the Spectral Efficiency of “One-Shot” Schemes	124
Efficient Localization via Soft Information With Generic Sensing Measurements	123
Adaptive Wireless Video Streaming: Joint Transcoding and Transmission Resource Allocation	123
Proactive Eavesdropping for Wireless Information Surveillance Under Suspicious Communication Quality-of-Service Constraint	123
Spinal Codes Over Fading Channel: Error Probability Analysis and Encoding Structure Improvement	123
Attacking and Defending Deep-Learning-Based Off-Device Wireless Positioning Systems	121
Unsourced Random Access Using Multiple Stages of Orthogonal Pilots: MIMO and Single-Antenna Structures	120
A Universal Framework for Multiport Network Analysis of Reconfigurable Intelligent Surfaces	120
Index Modulation for Fluid Antenna-Assisted MIMO Communications: System Design and Performance Analysis	119
Multi-Scenario Broadband Channel Measurement and Modeling for Sub-6 GHz RIS-Assisted Wireless Communication Systems	117
Reconfigurable Intelligent Surface Enabled Full-Duplex/Half-Duplex Cooperative Non-Orthogonal Multiple Access	116
Regularized Zero-Forcing Aided Hybrid Beamforming for Millimeter-Wave Multiuser MIMO Systems	115
A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization	115
Imperfect CSI Analysis in RIS-Aided Wireless Systems	111
Electromagnetic Channel Modeling and Capacity Analysis for HMIMO Communications	111
Task-Oriented Communication for Edge Video Analytics	111
An Online Zero-Forcing Precoder for Weighted Sum-Rate Maximization in Green CoMP Systems	111
Coexisting Passive RIS and Active Relay-Assisted NOMA Systems	110
Differential Modulation for Short Packet Transmission in URLLC	109
User Connection and Resource Allocation Optimization in Blockchain Empowered Metaverse Over 6G Wireless Communications	108
Data-Driven Caching With Users’ Content Preference Privacy in Information-Centric Networks	108
Performance Optimization on Cell-Free Massive MIMO-Aided URLLC Systems With User Grouping	108
SkyLink: Joint Deployment and Scheduling in Collaborative Integrated Ground-Air-Space Network	107
Fast-Adaptive Beamforming for Rate-Splitting Multiple Access-aided Space-Air-Ground Integrated Networks with Few-Shot Samples	106
Over-the-Air Computing With Imperfect CSI: Design and Performance Optimization	105

Symbiotic Radio With Orthogonal Time Frequency Space Modulation Over High-Mobility Channels	105
Joint Power Allocation and User Association Optimization for IRS-Assisted mmWave Systems	105
Passive Reflection Codebook Design for IRS-Integrated Access Point	104
CSI-Based Multi-Antenna and Multi-Point Indoor Positioning Using Probability Fusion	103
Joint Precoding for Active Intelligent Transmitting Surface Empowered Outdoor-to-Indoor Communication in mmWave Cellular Networks	103
Global Resource Allocation for High Throughput and Low Delay in High-Density VANETs	103
Positioning Using Visible Light Communications: A Perspective Arcs Approach	103
Self-Learning Based Computation Offloading for Internet of Vehicles: Model and Algorithm	103
Modeling and Analysis of Downlink Communications in a Heterogeneous LEO Satellite Network	101
A Hybrid Differential Detection Scheme for the Ultra-Wideband Orientational Beamforming System	101
Weighted Sum Rate Maximization of the mmWave Cell-Free MIMO Downlink Relying on Hybrid Precoding	100
Hybrid Analog/Digital Precoding for Downlink Massive MIMO LEO Satellite Communications	100
Federated Learning via Over-the-Air Computation With Statistical Channel State Information	100
Toward RIS-Aided Non-Coherent Communications: A Joint Index Keying M-ary Differential Chaos Shift Keying System	99
Robust Hybrid Beamforming Design for Multi-RIS Assisted MIMO System With Imperfect CSI	99
Learning the CSI Recovery in FDD Systems	99
Resource Management for MEC Assisted Multi-Layer Federated Learning Framework	99
Cooperative UAVs Placement Optimization for Best Multistatic Time-of-Arrival Localization in 5G Networks	98
Dynamic Role Switching Scheme With Joint Trajectory and Power Control for Multi-UAV Cooperative Secure Communication	98
An Energy-Efficient Aerial Backhaul System With Reconfigurable Intelligent Surface	97
SWIPT-Enabled MISO Ad Hoc Network Underlay RSMA-Based System With IRS	96
Optimization of IRS-Aided Sub-THz Communications Under Practical Design Constraints	95
Angle-Based Downlink Beam Selection and User Scheduling for Massive MIMO Systems	94
How to Proactively Monitor Untrusted Communications with Cell-Free Massive MIMO?	94
Channel Gain Map Estimation for Wireless Networks Based on Scatterer Model	94
Autonomous On-Demand Deployment for UAV Assisted Wireless Networks	93
Analysis of Age of Information in Dual Updating Systems	91
Delay-Phase Precoding for Wideband THz Massive MIMO	91
Cost-Optimal Deployment of Millimeter-Wave Base Stations Under Outage Requirement	91
Flexible Intelligent Metasurfaces for Downlink Multiuser MISO Communications	91
Channel Estimation for Movable Antenna Communication Systems: A Framework Based on Compressed Sensing	91
Federated Learning on the Road Autonomous Controller Design for Connected and Autonomous Vehicles	91
HDnGAN: A Channel Estimation Method for Time-Varying mmWave Massive MIMO	90
Waveform and Beamforming Design for Intelligent Reflecting Surface Aided Wireless Power Transfer: Single-User and Multi-User Solutions	90
Learning-Based Reliable and Secure Transmission for UAV-RIS-Assisted Communication Systems	90
Improving Cell-Free Massive MIMO Networks Performance: A User Scheduling Approach	89
Joint Power Allocation and Trajectory Design for UAV-Enabled Covert Communication	88
Deep Learning Assisted Multiuser MIMO Load Modulated Systems for Enhanced Downlink mmWave Communications	87
Affine Frequency Division Multiplexing for Next Generation Wireless Communications	87
Near-Field Wideband Beamforming for RIS-assisted THz Communications with FTTDs	86
Enhancing Secrecy Energy Efficiency in UAV-RIS Assisted Mobile IoV Networks Through DRL	86
Online Client Selection for Asynchronous Federated Learning With Fairness Consideration	85
Metasurface-Based Filters for High Data Rate THz Wireless Communication: Experimental Validation of a 14 Gbps OOK and 104 Gbps QAM-16 Wireless Link in the 300 GHz Band	83
Beam Focusing for Near-Field Integrated Sensing and Communications with Hybrid Analog/Digital Architecture	83
Deep Reinforcement Learning-Based Anti-Jamming Algorithm Using Dual Action Network	83
Latency Minimization for UAV-Enabled URLLC-Based Mobile Edge Computing Systems	82
Orthogonal Time Sequency Multiplexing Modulation: Analysis and Low-Complexity Receiver Design	81
Changeable Rate and Novel Quantization for CSI Feedback Based on Deep Learning	81
Table of Contents	80
Global Optimal Closed-Form Solutions for Intelligent Surfaces With Mutual Coupling: Is Mutual Coupling Detrimental or Beneficial?	80
Joint Vehicular Localization and Reflective Mapping Based on Team Channel-SLAM	79
A Deep Neural Architecture for Real-Time Access Point Scheduling in Uplink Cell-Free Massive MIMO	79
How Wireless Queues Benefit from Motion: An Analysis of the Continuum Between Zero and Infinite Mobility	79
IEEE Transactions on Wireless Communications Publication Information	79
Efficient Allocation of the Amount of Radio Resources in 5G NR to Efficient Allocation of Radio Resources in 5G NR	79
Moving Aerial Anchors Assisted Network Localization	78
Joint Multi-Branch Weighted Combining and Equalization Detector for Cooperative Communication	78
A Projective Geometric View for 6D Pose Estimation in mmWave MIMO Systems	78
Spectrally-Efficient Modulation on Conjugate-Reciprocal Zeros (SE-MOCZ) for Non-Coherent Short Packet Communications	77
STAR-RIS Aided Multi-Antenna NOMA Downlink and Uplink Transmissions: A Low-Complexity Approach	77
Optical Wireless Integrated Sensing and Communication Based on Optical Phased Array: Performance Metric and Optimal Beamforming	76
Globally Optimal Resource Allocation Design for Discrete Phase Shift IRS-Assisted Multiuser Networks With Perfect and Imperfect CSI	76
Exploiting Low-Density Signal Structure via Approximate Message Passing With Side Information for Grant-Free NOMA	76
System-Level Analysis of Full-Duplex Self-Backhauled Millimeter Wave Networks	76
New Game-Theoretic Approach to Decentralized Path Selection and Sleep Scheduling for Mobile Edge Computing	76
Power and Discrete Rate Adaptation in Wideband NOMA in Frequency-Selective Channels	76
A Heterogeneous 6G Networked Sensing Architecture With Active and Passive Anchors	75
QoS-Driven Load Balancing in Hybrid LiFi and WiFi Networks	75
IRS-Enabled Beam-Space Channel	75
Channel Norm-Based Energy Detection With Diversity Reception for Amplitude-Shift Keying in Rayleigh Fading	75
Index Modulation Pattern Design for Non-Orthogonal Multicarrier Signal Waveforms	75
UAV-RIS-Aided Space-Air-Ground Integrated Network: Interference Alignment Design and DoF Analysis	74
Joint Sensing and Age of Information Optimization for Energy Constrained UAV-Assisted Integrated Sensing, Calculation, and Communication	74
Personalized Federated Learning Over the Air	73
HF Skywave Massive MIMO Communication	73
Joint Physical and Network Layers Design for STARS-Assisted Multi-Cellular Edge Caching	72
Analysis of Wireless Communication Over Electromagnetic Impulse Noise Channel	72
Spectrum Sensing and SINR Estimation in IEEE 802.11s Cognitive Radio Ad Hoc Networks With Heterogeneous Interference	71
Joint Resource, Deployment, and Caching Optimization for AR Applications in Dynamic UAV NOMA Networks	71
Joint Offloading Decision and Trajectory Design for UAV-Enabled Edge Computing With Task Dependency	71

Efficient Multiuser AI Downloading via Reusable Knowledge Broadcasting	71
Integrated Sensing-Communication-Computation for Over-the-Air Edge AI Inference	71
A Fast Fuzzy DRL-Based Joint Beam Design and Power Allocation for Multi-Beam GEO-LEO Coexisting Satellite Networks	70
Reordered Amplitude Phase Shift Keying Aided Differential Spatial Modulation: DFDD-Based Low-Complexity Detector and Performance Analysis Over Fading Channels	70
Hybrid Position and Orientation Estimation for Visible Light Systems in the Presence of Prior Information on the Orientation	69
Secure Body-Centric Internet of Things Networks: Physical Layer Security versus Covert Communication	69
Modeling and Coverage Analysis of RIS-Assisted Integrated Sensing and Communication Networks	69
A Physics-Informed Deep Ray Tracing Network for Regional Channel Impulse Response Estimation	69
Coordinate Interleaved OFDM With Repeated In-Phase/Quadrature Index Modulation	68
Resource Allocation for Intelligent Reflecting Surface Assisted Wireless Powered IoT Systems With Power Splitting	68
Fundamentals of RIS-Aided Localization in the Far-Field	68
Intelligent Computation Offloading for Joint Communication and Sensing-Based Vehicular Networks	67
Modeling and Analysis of mmWave UAV Swarm Networks: A Stochastic Geometry Approach	67
Multi-RIS-Enabled 3D Sidelink Positioning	66
Multi Direction-of-Arrival Tracking Using Rigid and Flexible Antenna Arrays	66
Line-of-Sight MIMO via Intelligent Reflecting Surface	66
Semi-Passive Elements Assisted Channel Estimation for Intelligent Reflecting Surface-Aided Communications	65
Hybrid Driven Learning for Joint Activity Detection and Channel Estimation in IRS-Assisted Massive Connectivity	65
Analysis and Optimization of Wireless Federated Learning With Data Heterogeneity	64
Reliability Enhancement for VR Delivery in Mobile-Edge Empowered Dual-Connectivity Sub-6 GHz and mmWave HetNets	64
Low-Complexity CSI Feedback for FDD Massive MIMO Systems via Learning to Optimize	64
Digital Twin-Assisted Explainable AI for Robust Beam Prediction in mmWave MIMO Systems	63
A Non-Stationary Model With Time-Space Consistency for 6G Massive MIMO mmWave UAV Channels	63
Joint Communication and Computation for Federated Learning over Cell-Free MIMO Network	63
An Intelligent Coexistence Strategy for eMBB/URLLC Traffic in Multi-UAV Relay Networks via Deep Reinforcement Learning	63
A Novel Framework for User Positioning and Environment Sensing During Initial Random Access	62
Federated Learning via Intelligent Reflecting Surface	62
ROME: Robust Model Ensembling for Semantic Communication Against Semantic Jamming Attacks	62
An Optimization Framework for Federated Edge Learning	62
LTrust: An Adaptive Trust Model Based on LSTM for Underwater Acoustic Sensor Networks	62
System Design and Parameter Optimization for Remote Coverage From NOMA-Based High-Altitude Platform Stations (HAPS)	62
Semi-Data-Aided Channel Estimation for MIMO Systems via Reinforcement Learning	62
A Reliable Reinforcement Learning for Resource Allocation in Uplink NOMA-URLLC Networks	61
Coexisting Terahertz and RF Finite Wireless Networks: Coverage and Rate Analysis	61
Sparsity-Aware Intelligent Massive Random Access Control for Massive MIMO Networks: A Reinforcement Learning Based Approach	61
Cross-Channel Model-Driven Learning for Massive MIMO Detection by HyperNetwork	61
Interference Characterization and Mitigation for Multi-Beam ISAC Systems in Vehicular Networks	60
Delay Optimal Random Access With Heterogeneous Device Capabilities in Energy Harvesting Networks Using Mean Field Game	60
Bias-Reduced Closed-Form Method for 3-D Moving Object Localization by AOA Using Sensors at Known and Unknown Positions	60
Channel Orthogonalization With Reconfigurable Surfaces: General Models, Theoretical Limits, and Effective Configuration	60
Scalable User-Centric Distributed Massive MIMO Systems With Restricted Processing Capacity	60
Placement and Resource Allocation of Wireless-Powered Multiantenna UAV for Energy-Efficient Multiuser NOMA	59
Grant-Free Access via Bilinear Inference for Cell-Free MIMO With Low-Coherence Pilots	59
Adaptive Waveform Design for Communication-Enabled Automotive Radars	59
Air-to-Ground Communications Beyond 5G: UAV Swarm Formation Control and Tracking	59
Understanding Deep MIMO Detection	59
Location Information Assisted Beamforming Design for Reconfigurable Intelligent Surface Aided Communication Systems	59
An Adaptive Power Allocation for NOMA-Based Multi-Layer Satellite System	59
Cell-Free Massive MIMO With Finite Fronthaul Capacity: A Stochastic Geometry Perspective	58
Energy Efficiency Maximization of Massive MIMO Communications With Dynamic Metasurface Antennas	58
Positioning Security in 5G and Beyond: Model and Detection of Physical Layer Threats	58
Hybrid Reinforcement Learning for Joint Beamforming in STAR-RIS assisted CoMP Systems	58
Hybrid Beamforming for mmWave Integrated Sensing and Communication with Multi-static Cooperative Localization	58
Over-the-Air Federated Learning Over MIMO Channels: A Sparse-Coded Multiplexing Approach	58
Robust Transmission Design for Reconfigurable Intelligent Surface and Movable Antenna Enabled Symbiotic Radio Communications	58
Blockchain-Based Edge Collaboration With Incentive Mechanism for MEC-Enabled VR Systems	57
Precoding for Multi-Cell ISAC: From Coordinated Beamforming to Coordinated Multipoint and Bi-Static Sensing	57
Joint Localization and Signal Detection for Ambient Backscatter Communication Systems	57
Pilot Design and Signal Detection for Symbiotic Radio Over OFDM Carriers	57
Wireless-powered Multi-access Edge Computing with Cascaded zeRISs	57
Real-World Evaluation of Full-Duplex Millimeter Wave Communication Systems	57
Deep Reinforcement Learning-Based Resource Allocation for Integrated Sensing, Communication, and Computation in Vehicular Network	57
RIS Partition-Assisted Non-Orthogonal Multiple Access (NOMA) and Quadrature-NOMA With Imperfect SIC	57
Transceiver Design and Power Control for Full-Duplex Ultra-Reliable Low-Latency Communication Systems	57
Reconfigurable Intelligent Surface-Assisted Cell-Free Massive MIMO Systems Over Spatially-Correlated Channels	57
IRS-Assisted Aggregated VLC-RF System: Resource Allocation for Energy Efficiency Maximization	57
Massive MIMO With Dual-Polarized Antennas	57
Synergizing Beyond Diagonal Reconfigurable Intelligent Surface and Rate-Splitting Multiple Access	56
Deep Learning for Secure UAV Swarm Communication Under Malicious Attacks	56
Delay-Constrained Maximum Information Output Rate in Fading Channels	56
Integrated Sensing, Computation, and Communication: System Framework and Performance Optimization	55
Handoff-Aware Distributed Computing in High Altitude Platform Station (HAPS)–Assisted Vehicular Networks	55
VSLM: Virtual Signal Large Model for Few-Shot Wideband Signal Detection and Recognition	55
CoMP Transmission in Downlink NOMA-Based Cellular-Connected UAV Networks	55
Impact of Channel Aging on Cell-Free Massive MIMO Over Spatially Correlated Channels	55
Sparse Neural Network for Detection and Decoding of Non-Binary Polar-Coded SCMA	54
Fast Beam Training and Alignment for IRS-Assisted Millimeter Wave/Terahertz Systems	54
Multi-Agent Deep Reinforcement Learning for Massive Access in 5G and Beyond Ultra-Dense NOMA System	54
Blind Federated Learning at the Wireless Edge With Low-Resolution ADC and DAC	53
A Non-Stationary Channel Model for 6G Multi-UAV Cooperative Communication	53
Resource Reservation Coordination for Vehicle Platooning in C-V2X Networks	53
Mobile Edge Adversarial Detection for Digital Twinning to the Metaverse: A Deep Reinforcement Learning Approach	53
MUL-VR: Multi-UAV Collaborative Layered Visual Perception and Transmission for Virtual Reality	53
Dynamic Laser Inter-Satellite Link Scheduling Based on Federated Reinforcement Learning: An Asynchronous Hierarchical Architecture	53
Full-Duplex mmWave MIMO With Finite-Resolution Phase Shifters	53
Neural Codebook Design for MIMO Network Beam Management	52
Learning-Based Adaptive IRS Control With Limited Feedback Codebooks	52
Finite-Time Analysis of Over-the-Air Federated TD Learning	52
RIS Partitioning Based Scalable Beamforming Design for Large-Scale MIMO: Asymptotic Analysis and Optimization	52
Learning-Based Precoding-Aware Radio Resource Scheduling for Cell-Free mMIMO Networks	52
Pricing-Based Deep Reinforcement Learning for Live Video Streaming With Joint User Association and Resource Management in Mobile Edge Computing	52
Expectation Propagation Aided Signal Detection for Uplink Massive Generalized Spatial Modulation MIMO Systems	52
Graph Neural Network for Distributed Beamforming and Power Control in Massive URLLC Networks	51
Distributed Handoff Problem in Heterogeneous Networks With End-to-End Network Slicing: Decentralized Markov Decision Process-Based Modeling and Solution	51
Extreme Value Theory-Based Robust Minimum-Power Precoding for URLLC	51