The secrecy capacity of the MIMO wiretap channel

We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers. Our technique involves a careful study of a Sato-like upper bound via the solution of a certain algebraic Riccati equation.

• Publication year

  2007

• Venue

  2008 IEEE International Symposium on Information Theory

• Publication date

  2007-10-09

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1109/ISIT.2008.4595041arXiv 0710.1920
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel

  2010cited by this paper
• An MMSE Approach to the Secrecy Capacity of the MIMO Gaussian Wiretap Channel

  2009cited by this paper
• Secrecy capacity of independent parallel channels

  2009cited by this paper
• Wireless Information-Theoretic Security

  2008cited by this paper
• The Secrecy Capacity of the 2 × 2 MIMO Wiretap Channel

  2007cited by this paper
• A Note on the Secrecy Capacity of the Multi-antenna Wiretap Channel

  2007cited by this paper
• Secure Communication Over Fading Channels

  2007cited by this paper
• Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel

  2007cited by this paper
• The MIMOME Channel

  2007cited by this paper
• Multiple Antenna Secure Broadcast over Wireless Networks

  2007cited by this paper
• Towards the Secrecy Capacity of the Gaussian MIMO Wire-Tap Channel: The 2-2-1 Channel

  2007cited by this paper
• On the Gaussian MIMO Wiretap Channel

  2007cited by this paper
• Secret Communication via Multi-antenna Transmission

  2007cited by this paper
• Achievable Rates in Gaussian MISO Channels with Secrecy Constraints

  2007cited by this paper
• Secrecy Capacity Region of a Multiple-Antenna Gaussian Broadcast Channel With Confidential Messages

  2007cited by this paper
• An Extremal Inequality Motivated by Multiterminal Information-Theoretic Problems

  2007cited by this paper
• Secrecy Capacity of Wireless Channels

  2006cited by this paper
• On the Secrecy Capacity of Fading Channels

  2006cited by this paper
• Wireless Information-Theoretic Security - Part I: Theoretical Aspects

  2006cited by this paper
• Secrecy capacity of SIMO and slow fading channels

  2005cited by this paper
• Convex Optimization

  2004cited by this paper
• Secure space-time communication

  2003cited by this paper
• A survey of nonsymmetric Riccati equations

  2002cited by this paper
• Feedback can at most double Gaussian multiple access channel capacity

  1987cited by this paper
• The Gaussian wire-tap channel

  1978cited by this paper
• Broadcast channels with confidential messages

  1978cited by this paper
• The wire-tap channel

  1975cited by this paper
• Optimization by Vector Space Methods

  1968cited by this paper

• Physical Layer Security in Massive MIMO: Challenges and Open Research Directions Against Passive Eavesdroppers

  2026cites this paper
• Valuation of Physical Layer Security Under Jamming Attacks Utilizing RIS

  2025cites this paper
• Secrecy through Precoding: a Novel Physical Layer Encryption Scheme with Optimal PAPR

  2025cites this paper
• RIS-Empowered Jamming for Protected Zone Formation in In-Band Full Duplex Systems

  2025cites this paper
• Secure Communication in the Presence of an RIS-Enhanced Eavesdropper in MIMO Networks

  2025cites this paper
• The MIMO-ME-MS Channel: Analysis and Algorithm for Secure MIMO Integrated Sensing and Communications

  2025cites this paper
• Antenna Selection in MIMO–NOMA Systems: A New Approach for Physical Layer Security Enhancement

  2025cites this paper
• Secrecy Performance of a RIS-Assisted Wireless Network: A Comprehensive Analysis Under Outdated CSI

  2025cites this paper
• A Practical Algorithm for Physical Layer Encryption Under Constant Envelope Constraint

  2025cites this paper
• Linear and Numerical SDoF Bounds of Active RIS-Assisted MIMO Wiretap Interference Channel

  2025cites this paper
• Optimizing Indoor RIS-Aided Physical Layer Security: A Codebook-Generation Methodology and Measurement-Based Analysis

  2025cites this paper
• Static and Dynamic Finite Constellation Decomposition for Wireless Physical Layer Security

  2025cites this paper
• On Symbol Error Probability-based Beamforming in MIMO Gaussian Wiretap Channels

  2025cites this paper
• Enhancing Physical Layer Security Under Imperfect Quantized Feedback

  2025cites this paper
• Power Allocation Optimization for Secure OFDM-NOMA Downlink Systems

  2025cites this paper
• Covert Message Authentication in MIMO Communications

  2025cites this paper
• Decomposed and Distributed Directional Modulation for Secure Wireless Communication

  2024cites this paper
• Secrecy Analysis of ABCom-Based Intelligent Transportation Systems With Jamming

  2024cites this paper
• Compounding and Synchronization of Fractional Order Chaotic Systems With Prescribed Performance for Secure Communication

  2024cites this paper
• Integrating Physical Layer Security with Blockchain into Future Wireless Networks

  2024cites this paper
• Physical Layer Location Privacy in SIMO Communication Using Fake Path Injection

  2024cites this paper
• Lattice-Reduction-Aided Preprocessing for Physical-Layer Security

  2024cites this paper
• On Secret-Message Transmission by Echoing Encrypted Probes

  2024cites this paper
• Comparison of Optimization Criteria for Preprocessing for Physical-Layer Security in Multi-Carrier-THz-MIMO Systems

  2024cites this paper
• Phase Center Agile Array: a New Bistatic Radar Scheme for Encrypted Sensing

  2024cites this paper
• Beam-focusing in near-field communications: enhancing the physical layer security

  2024cites this paper
• Secret-Key Capacity From MIMO Channel Probing

  2024cites this paper
• Optimized Parameter Design for Channel State Information-Free Location Spoofing

  2024cites this paper
• Physical Layer Security for IRS-UAV-Assisted Cell-Free Massive MIMO Systems

  2024cites this paper
• Computational Secure Physical Layer Algorithm for MIMO Wireless Systems

  2024cites this paper
• Achieving Optimal Short-Blocklength Secrecy Rate Using Multi-Kernel PAC Codes for the Binary Erasure Wiretap Channel

  2024cites this paper
• Enhancing secrecy rates in visible-light communications with signal-dependent noise: exploring optical jamming technique

  2024cites this paper
• Physical Layer Security With Near-Field Beamforming

  2024cites this paper
• Securing Near-Field MIMO Communications via Dynamic Metasurface Antennas

  2024cites this paper
• Guaranteed Private Communication With Secret Block Structure

  2023cites this paper
• Minimum secrecy rate maximization for multiple peer-to-peer communications in two-way relaying networks

  2023cites this paper
• Physical Layer Security: Channel Sounding Results for the Multi-Antenna Wiretap Channel

  2023influential citation
• Enhancing Security in 6G Vehicular Networks: Leveraging VLC and MMW Integration and Cooperative Relaying Technique

  2023cites this paper
• EMF-Constrained Artificial Noise for Secrecy Rates With Stochastic Eavesdropper Channels

  2023cites this paper
• On the Sum Secrecy Rate of Multi-User Holographic MIMO Networks

  2023cites this paper
• Optimality of Proper Gaussian Signaling for SIMO Wiretap Channels

  2023cites this paper
• Exploring the effects of directional antennas on the secure connectivity and hop count of secure multi-hop ad-hoc wireless networks

  2023cites this paper
• The Security in Optical Wireless Communication: A Survey

  2023cites this paper
• Secure Transmission Scheme Based on Joint Radar and Communication in Mobile Vehicular Networks

  2023cites this paper
• Signal Strength Balanced Scheduling for Secure Ambient Backscatter Networks

  2023cites this paper
• Jamming and Eavesdropping Defense Scheme Based on Deep Reinforcement Learning in Autonomous Vehicle Networks

  2023cites this paper
• Secure Rate Splitting Multiple Access: How Much of the Split Signal to Reveal?

  2023cites this paper
• Friendly spectrum jamming against MIMO eavesdropping

  2022cites this paper
• Joint Precoding and Artificial Noise Design for MU-MIMO Wiretap Channels

  2022cites this paper
• K-Receiver Wiretap Channel: Optimal Encoding Order and Signaling Design

  2022cites this paper
• Optimal Order of Encoding for Gaussian MIMO Multi-Receiver Wiretap Channel

  2022cites this paper
• Extensions on 'A Convex Scheme for the Secrecy Capacity of a MIMO Wiretap Channel with a Single Antenna Eavesdropper'

  2022cites this paper
• Programmable Optical Data Transmission Through Multimode Fibres Enabling Confidentiality by Physical Layer Security

  2022cites this paper
• Detecting identity based spoofing attacks in wireless network using IDs

  2022cites this paper
• On the Capacity Achieving Input of Amplitude Constrained Vector Gaussian Wiretap Channel

  2022cites this paper
• Performance Improvement of Radio-Wave Encrypted MIMO Communications Using Average LLR Clipping

  2022cites this paper
• Security Gap Improvement of BICM Systems Through Bit-Labeling Optimization for the Gaussian Wiretap Channel

  2022cites this paper
• A Review of Fundamental Optimization Approaches and the Role of AI Enabling Technologies in Physical Layer Security

  2022cites this paper
• Multi-Level Encrypted Transmission Scheme Using Hybrid Chaos and Linear Modulation

  2022cites this paper
• A Secrecy Transmission Protocol with Energy Harvesting for Federated Learning

  2022cites this paper
• Improving MIMO Secrecy Rate through Efficient Power Allocation

  2022cites this paper
• Security–Reliability Tradeoff Analysis for SWIPT- and AF-Based IoT Networks With Friendly Jammers

  2022cites this paper
• Increasing Physical Layer Security Through Hyperchaos in VLC Systems

  2022cites this paper
• Counteracting Eavesdropper Attacks Through Reconfigurable Intelligent Surfaces: A New Threat Model and Secrecy Rate Optimization

  2022cites this paper
• Joint Secure Communication and Radar Beamforming: A Secrecy-Estimation Rate-Based Design

  2022cites this paper
• The 5G Cellular Downlink V2X Implementation Using V2N With Spatial Modulation

  2022cites this paper
• Directional modulation techniques for secure wireless communication: a comprehensive survey

  2022cites this paper
• Amplitude Constrained Vector Gaussian Wiretap Channel: Properties of the Secrecy-Capacity-Achieving Input Distribution

  2022cites this paper
• Large-Scale Rate-Splitting Multiple Access in Uplink UAV Networks: Effective Secrecy Throughput Maximization Under Limited Feedback Channel

  2022cites this paper
• Optimality of the Proper Gaussian Signal in Complex MIMO Wiretap Channels

  2022influential citation
• The Secrecy Capacity of The Gaussian Wiretap Channel with Rate-Limited Help at the Decoder

  2022cites this paper
• Cognitive Risk Control for Anti-Eavesdropping in Connected and Autonomous Vehicles Network

  2022cites this paper
• Interference Signal Superposition-aided MIMO with Antenna Number Modulation and Adaptive Antenna Selection for Achieving Perfect Secrecy

  2021cites this paper
• Robust Secure Transmit Design with Artificial Noise in the Presence of Multiple Eavesdroppers

  2021cites this paper
• Information-Theoretically Secure String Commitments Based on Packet Reordering Channels

  2021cites this paper
• Secure Communication for Spatially Correlated Massive MIMO With Low-Resolution DACs

  2021cites this paper
• Physical Layer Security Optimization for MIMO Enabled Visible Light Communication Networks

  2021cites this paper
• Secrecy Rate Maximization for Intelligent Reflecting Surface Assisted MIMOME Wiretap Channels

  2021cites this paper
• Antenna Grouping-Based Blind Artificial Noise for TDD Secure Transmission

  2021cites this paper
• Secrecy-Capacity Bounds for Visible Light Communications With Signal-Dependent Noise

  2021cites this paper
• Secrecy-Capacity-Optimization-Artificial-Noise in Large-Scale MIMO: Ergodic Lower Bound on Secrecy Capacity and Optimal Power Allocation

  2021cites this paper
• Joint Active and Passive Secure Precoding in IRS-Aided MIMO Systems

  2021cites this paper
• Quantization-Aided Secrecy: FD C-RAN Communications With Untrusted Radios

  2021cites this paper
• Finite Blocklength Secrecy Analysis of Polar and Reed-Muller Codes in BEC Semi-Deterministic Wiretap Channels

  2021cites this paper
• Intelligent reflecting surface assisted MIMO communication system: A review

  2021cites this paper
• Research on Physical Layer Encryption Technology of HST 5G communication system with spatial permutation modulation

  2021cites this paper
• Secrecy Performance of Eigendecomposition-Based FTN Signaling and NOFDM in Quasi-Static Fading Channels

  2021cites this paper
• Designing IRS-Aided MIMO Systems for Secrecy Enhancement

  2021cites this paper
• Physical Layer Security for Multi-User MIMO Visible Light Communication Systems With Generalized Space Shift Keying

  2021cites this paper
• Reconfigurable Intelligent Surfaces-Aided Physical Layer Security Enhancement in D2D Underlay Communications

  2021cites this paper
• An Overview of Information-Theoretic Security and Privacy: Metrics, Limits and Applications

  2021cites this paper
• On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel

  2021influential citation
• Efficient Numerical Methods for Secrecy Capacity of Gaussian MIMO Wiretap Channel

  2021cites this paper
• Deep Learning Based Robust Beamforming for UAV Communication System

  2021cites this paper
• Joint Beamforming Optimization for the Intelligent Reflecting Surface Assisted Wireless Surveillance System

  2021cites this paper
• QoS-Aware Secure Routing Design for Wireless Networks With Selfish Jammers

  2021cites this paper
• Artificial Noise-Aided MIMO Physical Layer Authentication With Imperfect CSI

  2021cites this paper
• Improvement of Channel Coding Gain of Chaos Modulation Using Logistic Maps

  2021cites this paper
• Securing Massive MIMO Systems: Secrecy for Free With Low-Complexity Architectures

  2021cites this paper
• Physical Layer Security of In-Home PLC Systems: Analysis Based on a Measurement Campaign

  2021cites this paper