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A Survey of Optimization Approaches for Wireless Physical Layer Security
Dong Wang, Bo Bai, Wenbo Zhao, Zhu Han
TL;DR
Wireless physical-layer security research spans information-theoretic secrecy analysis and optimization-based transmission design, with the latter needing a comprehensive synthesis. This survey organizes wiretap models, secure design topics, metrics, optimization problem classes, CSI impacts, and future challenges. It concludes that practical applicability remains constrained by assumptions about CSI, eavesdroppers, and deployment scenarios.
Problem
Physical-layer security requires a comprehensive account of optimization and signal-processing designs beyond research focused on secrecy capacity and achievable secrecy rate.
Method
The survey synthesizes wiretap channel models, secure design topics, performance metrics, optimization approaches, CSI impacts, and future directions.
Results
The survey provides a well-rounded overview of optimization and design in physical-layer security for newcomers.
Takeaways & Limitations
Physical-layer security design is organized around resource allocation, beamforming/precoding, antenna or node selection, cooperation, and four recurring optimization objectives.
Takeaways & Limitations
Practical secure-transmission optimization is constrained when wiretap-channel CSI is unavailable because instantaneous secrecy rate cannot be determined.
Abstract
from arXiv · showhide
Due to the malicious attacks in wireless networks, physical layer security has attracted increasing concerns from both academia and industry. The research on physical layer security mainly focuses either on the secrecy capacity/achievable secrecy rate/capacity-equivocation region from the perspective of information theory, or on the security designs from the viewpoints of optimization and signal processing. Because of its importance in security designs, the latter research direction is surveyed in a comprehensive way in this paper. The survey begins with typical wiretap channel models to cover common scenarios and systems. The topics on physical-layer security designs are then summarized from resource allocation, beamforming/precoding, and antenna/node selection and cooperation. Based on the aforementioned schemes, the performance metrics and fundamental optimization problems are discussed, which are generally adopted in security designs. Thereafter, the state of the art of optimization approaches on each research topic of physical layer security is reviewed from four categories of optimization problems, such as secrecy rate maximization, secrecy outrage probability minimization, power consumption minimization, and secure energy efficiency maximization. Furthermore, the impacts of channel state information on optimization and design are discussed. Finally, the survey concludes with the observations on potential future directions and open challenges.
I. INTRODUCTION
Physical layer security uses the randomness of wireless channels to complement cryptographic security, while this survey focuses on optimization and signal-processing designs. It organizes the field around channel models, design topics, performance metrics, optimization approaches, CSI assumptions, and future challenges.
- Motivation: Physical layer security complements upper-layer cryptography by exploiting wireless-medium randomness, avoiding reliance on keys for physical-layer secrecy.Cryptographic methods can incur heavy computation and key-management costs, while wiretap models achieve secrecy through differences between legitimate and illegitimate channels.
- Research scope: Research divides between information-theoretic secrecy capacity analysis and practical security designs based on optimization and signal processing.The survey concentrates on the second direction while retaining the information-theoretic security framework underlying its metrics and designs.
- Survey coverage: The survey covers secure resource allocation, beamforming/precoding, antenna and node selection, and cooperation across common wiretap-channel scenarios.Its introductory models include MIMO, broadcast, multiple-access, interference, and relay wiretap channels.
- Optimization framework: It reviews performance metrics and optimization approaches organized around secrecy-rate maximization, secrecy-outage minimization, power-consumption minimization, and secure-energy-efficiency maximization.These metrics and problem classes are presented as tools for evaluating and designing secure transmission strategies.
- Challenges and outlook: The survey highlights CSI assumptions, future directions, and open challenges as important boundaries for practical physical-layer security designs.The paper discusses the effects of CSI on secure transmission and concludes with directions for improving applicability to emerging wireless networks.
1) MIMO wiretap channels:
The survey presents wiretap channel models for single-link, broadcast, multiple-access, interference, and cooperative relay scenarios. These models specify legitimate and eavesdropping links, antenna configurations, signals, channel matrices, and noise.
- MIMO wiretap channels: The MIMO wiretap channel models a transmitter, legitimate receiver, and eavesdropper, with SISO, SIMO, and MISO channels as special cases.The transmitter, receiver, and eavesdropper use nt, nd, and ne antennas, respectively.
- Broadcast wiretap channels: Broadcast wiretap channels describe one multiantenna transmitter sending confidential messages to multiple users while preventing interception by multiple eavesdroppers.The model includes I legitimate users and J eavesdroppers and can represent several special cases.
- Multiple-access wiretap channels: Multiple-access wiretap channels contain multiple transmitters communicating with one legitimate receiver in the presence of an eavesdropper.Each transmitter has its own channel matrices and signal, subject to covariance or average-power constraints.
- Interference wiretap channels: Interference wiretap channels involve multiple simultaneously active links whose transmissions interfere and are overheard by an eavesdropper.The model uses K source-destination pairs and channel matrices from each source to destinations and the eavesdropper.
- Relay wiretap channels: Cooperative relay wiretap channels include a source, destination, relay, and eavesdropper, with decode-and-forward and amplify-and-forward relay models studied.In decode-and-forward operation, the relay first receives and decodes the source signal, then forwards a re-encoded version to the destination.
B. Concepts of Optimization
The survey introduces optimization as the search for design variables that optimize an objective under constraints, distinguishing convex problems from generally harder nonconvex problems. Physical-layer security designs use transformations and specialized algorithms for metrics and variables arising in secure transmission.
- General optimization: A general optimization problem minimizes an objective over variables satisfying inequality and equality constraints.The optimal solution is the feasible variable set that minimizes f(x).
- Convex optimization: Convex optimization requires convex objectives and inequality constraints, while equality constraints must be affine.Interior-point methods can solve convex problems optimally, motivating transformations of practical problems into convex form.
- Nonconvex optimization: Nonconvex optimization includes nonconvex objectives or constraints and can have global-solution complexity that grows exponentially with problem size.Some nonconvex problems are transformed or approximated by convex problems, while heuristic algorithms can provide approximate solutions.
- Optimization in physical-layer security: Physical-layer security optimization variables include resources, beamformers or precoders, and candidate antennas or cooperative nodes.Objectives include secrecy rate or capacity, secrecy outage probability or capacity, power consumption, and secure energy efficiency.
- Optimization problem classes: Secure designs use integer, mixed-integer, DC, quadratic, and semidefinite programming for allocation, selection, secrecy-rate, power, and beamforming problems.Semidefinite programming is often obtained by transforming nonconvex problems into efficiently solvable formulations.
- Optimization approaches: Fractional programming targets ratios of nonlinear functions, including secure energy-efficiency maximization.Other techniques include dual decomposition, alternating search, penalty functions, SPCA, and SDR.
III. RESEARCH TOPICS ON SYSTEM DESIGNS OF PHYSICAL LAYER SECURITY
Physical-layer security system designs focus on resource allocation, beamforming and precoding, and their joint use in multiantenna and multinode networks. These approaches adjust resources, spatial transmission, artificial noise, and transmission candidates to improve secure performance.
- Secure Resource Allocation: Secure resource allocation uses frequency, timeslot, and power resources to enlarge the difference between legitimate and wiretap channels.Subcarrier allocation is generally binary, while adaptive power allocation and joint allocation address different design requirements.
- Secure Resource Allocation: Joint subcarrier and power allocation is usually a mixed-integer nonlinear optimization problem and is NP-hard in most situations.Practical studies therefore use optimization techniques that provide simple and suboptimal solutions.
- Secure Beamforming and Precoding: Secure beamforming and precoding optimize spatial transmission to improve the destination signal while reducing the eavesdropper signal.Beamforming transmits one data stream, whereas precoding supports multiple streams and beamforming is a special case of precoding.
- Secure Beamforming and Precoding: Null-space beamforming suppresses transmission at the eavesdropper, while MRT uses low-complexity channel-based transmission to improve the intended receiver’s SNR.MRT requires knowledge of the channel from the transmitter to the intended receiver and can approach channel capacity in low-SNR scenarios when combined with MRC.
- Secure Beamforming and Precoding: Precoding spatially multiplexes confidential messages over independent subchannels while optimizing security metrics and maintaining QoS.CI or ZF precoding cancels signals leaked to unintended users, while regularized CI trades off signal power and interference.
- Secure Beamforming and Precoding: Artificial-noise strategies superimpose AN on transmitted signals to deteriorate eavesdropper reception, with AN vectors also subject to global optimization.The approach is also called masked beamforming or masked precoding in relevant wiretap channels.
C. Antenna/Node Selection and Cooperation
Antenna and node selection exploit spatial diversity and channel variation to improve secure transmission while saving resources. Relay and jammer cooperation, together with joint design strategies, broadens the available security-performance trade-offs.
- Antenna/Node Selection and Cooperation: Antenna and node selection chooses suitable candidates to improve secure transmission performance while saving resources.Node selection includes users, relays, and jammers.
- Antenna/Node Selection and Cooperation: Transmit antenna selection reduces hardware complexity, radio-frequency insertion losses, and feedback overhead in large-array MIMO systems.It also exploits spatial degrees of freedom for physical-layer security.
- Antenna/Node Selection and Cooperation: User selection schedules users for confidential transmission by exploiting spatial diversity from independently varying user locations and channel attenuation.The best-channel user can improve secrecy rate or throughput, but this selection depends on legitimate and wiretap channels.
- Antenna/Node Selection and Cooperation: Relay selection can exploit distributed relay nodes’ spatial degrees of freedom to improve secure QoS and potentially maximize secrecy capacity.Cooperative relaying with relay selection can also benefit rate and energy efficiency.
- Antenna/Node Selection and Cooperation: Cooperative jamming selects trusted or untrusted intermediate nodes to transmit artificial interference that confuses eavesdroppers.Untrusted nodes require careful use because they may themselves be potential eavesdroppers.
- Antenna/Node Selection and Cooperation: Joint relay and jammer selection assigns some intermediate nodes to relay confidential data and others to jam potential eavesdroppers.The survey describes this joint method as more effective for whole-network secure performance than either single approach.
- Joint Strategies and Metrics: Joint strategies combine resource allocation, scheduling, antenna selection, beamforming, precoding, and jamming for secrecy improvements in specific scenarios.The survey evaluates designs using secrecy rate or capacity, secrecy outage probability or capacity, power consumption, and secure energy efficiency.
A. Secrecy Rate/Capacity
Secrecy rate measures confidential throughput, while secrecy capacity gives its upper bound under reliable and secure transmission. Optimization designs seek to maximize achievable secrecy rate using resource allocation, beamforming, precoding, and cooperation under power constraints.
- Secrecy rate measures the secret bits transmitted per second over a given channel and is commonly optimized under channel fading.Achievable secrecy rate is typically used as an optimization objective in secure transmission designs.
- Secrecy capacity is the upper bound on secrecy rate for secure and reliable transmission against eavesdroppers.For degraded wiretap channels, capacity can be achieved through an optimal channel-input distribution.
- In non-degraded wiretap channels, secrecy capacity is characterized by optimizing over joint distributions involving an auxiliary variable V.The variables form the Markov chain V → X → (Y, Z).
- Achievable secrecy rate is optimized by adjusting resources, beamforming/precoding, cooperative diversity, or other optimization variables.The objective is to maximize the confidential throughput as much as possible.
- Power constraints in secrecy-rate maximization may apply to the total network or individually to each transmission node.In relay networks, beamforming can replace power variables with relay weight vectors while strengthening desired signals and suppressing undesired directions.
B. Secrecy Outage Probability/Capacity
Secrecy outage metrics quantify failures caused by fading and imperfect channel knowledge, providing explicit measures of secure-transmission reliability. Optimization therefore minimizes outage probability under resource constraints or maximizes outage capacity for a tolerable outage level.
- Secrecy outage probability measures the probability that secure transmission cannot be achieved because a secrecy outage event occurs.Channel fading and imperfect CSI can break secure transmission.
- The common outage definition declares failure when instantaneous secrecy capacity falls below a target secrecy rate.Such events include insufficient legitimate-channel support for the target rate.
- This capacity-based outage definition combines reliability failure and information leakage, so it does not distinguish the two conditions.An outage under this definition does not necessarily imply failure to achieve perfect secrecy.
- A second definition conditions outage on message transmission and evaluates whether the secrecy overhead is insufficient against the eavesdropper channel.With legitimate-channel CSI, transmission decisions and variable rates can reduce the conditional outage probability.
- Secrecy outage capacity is the largest secrecy rate supportable while keeping secrecy outage probability below a tolerable level ε.Outage formulations help evaluate the security level of a proposed transmission scheme.
- Secrecy outage minimization seeks the lowest outage probability subject to resource constraints such as per-node peak-power limits.The peak-power constraint limits excessive consumption while improving secrecy rate.
C. Power/Energy Consumption
Power and energy consumption are central metrics for secure communications in resource-limited networks because secrecy can require additional power and relay cooperation can add circuit costs. Power-minimization designs adjust transmit levels to meet secrecy, reliability, or quality-of-service requirements.
- Power and energy consumption are primary design metrics for sustaining secure communications and prolonging network lifetime in resource-limited networks.Battery-dependent and energy-harvesting systems especially motivate these objectives.
- Total wireless-system consumption includes power-amplifier consumption and other circuit-block consumption.Amplifier consumption depends on output transmit power and amplifier efficiency, while circuit costs include transmitter, receiver, and baseband components.
- Cooperative relay models account for source and relay transmission powers, circuit powers, relay-node sets, and half-duplex operation.The total-power formulation can therefore differ across practical network settings.
- Secure transmission can consume more power than conventional communication because secure coding reduces confidential-message rate and stronger secrecy requires additional energy.Relay cooperation may also introduce extra circuit-power consumption.
- Power minimization seeks the minimum consumption needed to satisfy requirements such as target secrecy rate, destination SNR, secrecy probability, or other QoS constraints.The formulation is applied across secure transmission designs, including relay networks.
- Beamforming-based power minimization determines total power through the beamformer weights.The general power model is a starting point that can be specialized for practical applications.
D. Secure EE
Secure energy efficiency evaluates confidential throughput relative to energy use, linking secrecy performance with green communications. Its optimization must account for secure QoS and comprehensive network power consumption rather than transmission power alone.
- Secure energy efficiency is the amount of secret information transmitted per unit energy and is optimized to increase confidential throughput for a given energy budget.It is also called secret bits per Joule.
- Secure energy efficiency equals secrecy rate divided by total power consumption.This ratio is frequently used to evaluate energy efficiency in physical-layer secure communications.
- Energy per secret bit is the reciprocal metric, measuring the minimum energy required to transmit one secret bit reliably under secrecy constraints.The two metrics lead generally to dual optimization problems.
- A holistic secure-energy-efficiency model should include transmission power, circuit power, and signaling overhead across the network.Traditional models that consider transmission power alone are insufficient for system-wide accounting.
- Secure communications may consume more power and energy than conventional communications because protecting confidential information creates additional cost.This burden is especially relevant in power- and energy-limited scenarios.
- Secure energy-efficiency optimization should satisfy a minimum secrecy-rate QoS requirement.The requirement is expressed as Rs ≥ R0_s.
V. THE STATE OF THE ART OF OPTIMIZATION AND DESIGN
The survey organizes physical-layer security designs around four optimization objectives and reviews resource-allocation methods across secrecy-rate and outage-oriented formulations. These approaches include mixed-integer programming, probabilistic allocation, closed-form power solutions, and dual decomposition.
- The state of the art is organized into secrecy rate maximization, secrecy outage probability minimization, power consumption minimization, and secure EE maximization.
- Secure resource allocation assigns frequency, time, and power resources to improve secrecy performance under scenario-specific constraints.
- Secrecy-rate maximization in multicarrier systems commonly allocates limited power and subcarriers across transmission nodes, producing mixed integral programs.
- Relay-aided multicarrier allocation uses binary source and relay transmission indicators to determine whether each carrier supports direct, relay, or no communication.
- Dual decomposition converts constraints into a weighted Lagrangian objective, separates the problem into distributed subproblems, and coordinates them through iterative master-level optimization.
- Outage minimization includes probabilistic subcarrier allocation, closed-form power allocation, and joint optimization of transmission power, artificial-noise splitting, or node placement.
3) Minimization of power consumption:
Power-consumption minimization designs seek the least energy expenditure that satisfies secure QoS requirements, while accounting for the extra cost of artificial noise and jamming. The surveyed formulations span resource allocation, network types, and energy–secrecy tradeoffs.
- Secure resource allocation minimizes power while satisfying secure QoS requirements, but artificial noise and jamming improve wiretap protection at additional energy cost.
- Power-efficient designs cover multiuser MISO, non-orthogonal multiple access, and heterogeneous macro–small-cell communication scenarios.
- Secure energy-efficiency studies optimize power, secrecy rate, subcarrier allocation, access probability, or power splitting across multiple-access, relay, cognitive-radio, and multi-antenna networks.
- Energy-efficient multi-antenna designs explicitly consider perfect CSI, partial CSI, and statistical CSI, with artificial-noise extensions and metrics including secret bits per Joule.
- Secure energy-efficiency formulations are often nonconvex and are addressed using fractional programming, penalty methods, alternating optimization, and DC programming.
- Some designs optimize weighted products of secure energy efficiency and spectral efficiency to balance energy use and secrecy.
1) Maximization of achievable secrecy rate:
Beamforming and precoding exploit multi-antenna and cooperative-network structure to improve secrecy, reduce outage or power consumption, and increase secure energy efficiency. Designs range from simple MRT and artificial-noise schemes to optimized nonconvex precoders.
- Conventional beamforming/precoding: Conventional schemes combine MRT, artificial-noise null-space beamforming, and GSVD, with power allocation optimized for secrecy improvements.
- Conventional beamforming/precoding: MRT strengthens intended-user signals, null-space artificial noise disrupts eavesdroppers without affecting legitimate channels, and zero forcing uses eavesdropper CSI to limit leakage.
- Optimal beamforming/precoding: Optimal precoding formulates secrecy-capacity maximization under maximum-power and positive-semidefinite constraints, then applies alternating optimization and dual decomposition.
- Optimal beamforming/precoding: Alternating optimization separates source and relay beamforming in MIMO relay networks, with semidefinite programming used for resulting subproblems.
- Secrecy outage and power objectives: Beamforming and precoding also target secrecy-outage minimization through location-based designs and iterative hybrid precoding under partial channel knowledge.
- Secrecy outage and power objectives: Power-minimization designs jointly optimize source power, relay weights, base-station precoders, and friendly-jammer covariance while enforcing secrecy-rate or SINR constraints.
4) Maximization of secure EE:
Antenna and node selection exploit spatial or multiuser diversity to improve secrecy performance across rate, outage, power, and energy-efficiency objectives. Cooperative relays strengthen legitimate links, jammers degrade wiretap links, and hybrid designs combine both roles.
- Maximization of achievable secrecy rate: Antenna selection provides secrecy-rate gains through multi-antenna diversity, while user selection exploits multiuser diversity in multiuser systems.
- Maximization of achievable secrecy rate: Cooperative relaying retransmits confidential data to improve legitimate reception, whereas cooperative jamming emits interference to degrade eavesdropper channels.
- Maximization of achievable secrecy rate: Hybrid relaying and jamming divides intermediate nodes into relays and jammers, combining destination signal improvement with eavesdropper disruption.
- Maximization of achievable secrecy rate: Relays can forward confidential information and transmit artificial noise simultaneously, using their available degrees of freedom more fully.
- Minimization of secrecy outage probability: Antenna, relay, jammer, and user-pair selection are studied to reduce secrecy outage probability across MIMOME, relay, NOMA, and cognitive-radio systems.
- Minimization of power consumption: Cooperation can increase power consumption when nodes provide little secrecy benefit, motivating selection strategies that preserve secure QoS while reducing energy use.
4) Maximization of secure EE:
Secure energy-efficiency designs include antenna/node selection and cooperation, but their optimization depends strongly on channel-state information and assumptions about wireless channels. Unknown or imperfect eavesdropper CSI therefore motivates probabilistic, QoS-based, and robust secure designs.
- Secure EE designs: Antenna/node selection and cooperation can provide secure energy-efficiency gains in cooperative MIMO relay and activation-game settings.Examples include transmit antenna selection with maximal-ratio combining, jammer-only or relay-based cooperation, and node activation strategies.
- CSI assumptions: Perfect CSI of legitimate and wiretap channels is important for choosing secrecy metrics and designing optimal secure transmissions.Perfect all-channel CSI supports instantaneous secrecy-rate calculations and optimization, while legitimate-channel CSI is generally easier to obtain than wiretap-channel CSI.
- CSI assumptions: Wiretap-channel uncertainty can be modeled statistically, deterministically, or through an imperfect estimate with a channel-knowledge parameter κ.In the κ model, κ = 1 denotes perfect eavesdropper CSI and κ = 0 denotes no eavesdropper CSI.
- Unknown CSI: When eavesdropper CSI is unknown, instantaneous secrecy rate and instantaneous optimization are unavailable, so probabilistic-security or QoS-based designs are used instead.Reported metrics and designs include non-zero secrecy-capacity probability, secrecy outage probability, ε-outage secrecy capacity, QoS-constrained secrecy sum-rate maximization, and QoS-based cooperative relaying.
- Open challenges: Existing secure-design studies often rely on special CSI, eavesdropper, and application assumptions that may be impractical, while channel correlations, mobility, and estimation overhead remain open challenges.Accurate wiretap-channel estimation can require substantial pilot overhead and power, especially in massive MIMO, and may be vulnerable to pilot contamination attacks.
B. The Impacts of Adversary Model
Physical-layer security designs must address increasingly complex adversaries, practical hardware constraints, imperfect channel information, and difficult cross-layer optimization problems. The survey identifies these conditions as open challenges for secure deployment in emerging and commercial wireless networks.
- B. The Impacts of Adversary Model: Hybrid attacks such as eavesdropping, jamming, denial of service, spoofing, and message falsification complicate physical-layer security optimization.The survey calls for techniques that jointly defend against these attack types.
- B. The Impacts of Adversary Model: Intelligent adversaries may collaborate, manipulate the propagation environment, learn network weaknesses, and adapt their attacks.Developing effective secure mechanisms against such adversaries remains challenging.
- C. The Influences of Hardware Impairments: Hardware impairments from nonlinear amplifiers, I/Q imbalance, offsets, quantization noise, and synchronization errors challenge secure transmission assumptions.These issues become especially significant in massive MIMO, mm-Wave, and full-duplex systems.
- E. The Global Optimization with Security, Reliability, and Throughput: Joint security, reliability, and throughput optimization is difficult because these metrics interact and are often treated separately.Adding energy-efficiency requirements makes the resulting global optimization even more complicated.
- VIII. CONCLUSIONS: Physical-layer security remains largely theoretical, while commercial deployment faces technical flaws, network-architecture constraints, and rapidly changing wireless channels.Emerging settings such as high-speed mobile networks, device-to-device communications, cognitive radio, and IoT require fast CSI evaluation and dynamic authentication.
- VIII. CONCLUSIONS: Imperfect eavesdropper CSI prevents many designs from relying on perfect channel knowledge and motivates robust, probabilistic, or QoS-based approaches.The survey also highlights eavesdropper models, hardware impairments, cross-layer designs, global optimization, and commercial application as open challenges.