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On the Throughput Cost of Physical Layer Security in Decentralized Wireless Networks

Xiangyun Zhou, Radha Krishna Ganti, Jeffrey G. Andrews, Are Hjørungnes

arXiv:1012.4552v3cs.IT

TL;DR

The paper asks when decentralized wireless networks can achieve positive secrecy transmission capacity and how much throughput security requires. It applies the transmission-capacity framework and finds that moderate security has relatively low throughput cost, whereas highly secure operation can require substantial sacrifice; guard zones improve throughput under stringent security requirements.

  • Problem

    The paper examines the condition under which decentralized wireless networks can achieve positive secrecy transmission capacity, addressing a research area with few prior studies.

  • Method

    The paper uses transmission capacity to characterize secure-network area spectral efficiency under physical-layer security requirements.

  • Results

    Moderate security has relatively low throughput cost, while improving security toward ϵ = 0 can reduce τ LB(r) by 84%; guard zones increase ϵ = 0.01 from 0.003 at D = 0 to 0.018 with non-cooperative and 0.021 with cooperative protocols at D = 3.

  • Takeaways & Limitations

    Guard zones provide a significant throughput improvement when security requirements are high, while highly secure operation entails substantial throughput sacrifice.

  • Takeaways & Limitations

    The paper identifies limitations of its model and notes another limitation concerning physical-layer-security networks as an open problem.

Abstract

from arXiv · show

This paper studies the throughput of large-scale decentralized wireless networks with physical layer security constraints. In particular, we are interested in the question of how much throughput needs to be sacrificed for achieving a certain level of security. We consider random networks where the legitimate nodes and the eavesdroppers are distributed according to independent two-dimensional Poisson point processes. The transmission capacity framework is used to characterize the area spectral efficiency of secure transmissions with constraints on both the quality of service (QoS) and the level of security. This framework illustrates the dependence of the network throughput on key system parameters, such as the densities of legitimate nodes and eavesdroppers, as well as the QoS and security constraints. One important finding is that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network. We also study the use of a secrecy guard zone, which is shown to give a significant improvement on the throughput of networks with high security requirements.

I. INTRODUCTION

Prior physical-layer security studies largely focused on small-node or specialized channel settings, leaving large-scale decentralized networks comparatively understudied. Existing connectivity and scaling results do not provide the finer throughput view needed to assess system-parameter and protocol effects.

  • Few physical-layer security studies had addressed large-scale wireless networks.
  • Security is more difficult and expensive in large-scale decentralized networks than in point-to-point communications.
  • Unknown eavesdropper locations become additional parameters affecting network throughput.
  • Prior random-network work characterized secure connectivity, coverage, and capacity scaling laws.
  • Connectivity results establish whether secure communication is possible but do not reveal network throughput.
  • A finer throughput view is needed because design choices can affect throughput without changing scaling behavior.

A. Approach and Contributions

The paper extends transmission-capacity analysis to secure decentralized networks, defining secrecy transmission capacity under QoS and security constraints. It derives a Rayleigh-fading lower bound, quantifies security-related throughput costs, and evaluates secrecy guard zones.

  • The paper characterizes throughput for secure communications in large wireless networks.
  • Secrecy transmission capacity measures successful confidential-message rate per unit area under connection-outage and secrecy-outage constraints.
  • The framework models legitimate nodes and eavesdroppers using homogeneous Poisson point processes and relates area spectral efficiency to their densities and constraints.
  • For Rayleigh fading, the paper derives an accurate closed-form lower bound that quantitatively characterizes physical-layer-security throughput cost.
  • Moderate security has relatively small throughput cost, whereas highly secure operation requires significant throughput sacrifice.
  • A secrecy guard zone can significantly improve throughput in networks with high security requirements.

II. SYSTEM MODEL AND CAPACITY FORMULATION

The system model represents decentralized ad hoc networks with legitimate transmitters and eavesdroppers, and formulates secure throughput through connection and secrecy outage constraints. The resulting secrecy transmission capacity captures successful confidential-message rate per unit area.

  • Each legitimate transmitter has one associated intended receiver, while eavesdroppers form a separate location set.
  • Legitimate nodes and eavesdroppers are modeled as independent homogeneous two-dimensional Poisson point processes.
  • Wyner coding uses transmitted-codeword rate Rt and confidential-message rate Rs, with Re = Rt − Rs representing security overhead.
  • Connection outage occurs when the intended link cannot support Rt, whereas secrecy outage occurs when an eavesdropper link exceeds Re.
  • The secrecy transmission capacity is the achievable successful confidential-message rate per unit area under specified connection- and secrecy-outage constraints.
  • The formulation assumes fixed transmit power and transmitter-receiver distance, while also describing how a known distance distribution could be incorporated.

III. SECRECY TRANSMISSION CAPACITY IN RAYLEIGH FADING CHANNELS

For Rayleigh fading, the paper derives bounds and a closed-form lower bound for secrecy transmission capacity using connection and secrecy outage constraints. The analysis shows that stricter security reduces throughput and that guard zones can mitigate this cost.

  • The analysis assumes single-antenna Rayleigh fading with path-loss exponent α > 2 and interference treated as noise.
  • The connection-outage constraint determines Rt, and lower connection-outage probability requires lower Rt.
  • Secrecy-outage bounds are derived using the eavesdropper point process, Jensen’s inequality, and the nearest-eavesdropper event.
  • The upper secrecy-outage bound is an accurate approximation across the entire Pso range, while both bounds are asymptotically tight at low probabilities.
  • A lower secrecy-outage probability requires higher Re, and the resulting secrecy-capacity lower bound decreases as security becomes stricter.
  • The closed-form secrecy-capacity characterization lets designers optimize system parameters for maximum secure-transmission throughput at a target security level.

A. Existence of Positive Secrecy Transmission Capacity

Positive secrecy transmission capacity requires a condition linking the QoS and secrecy constraints. When feasible, an optimal legitimate-node transmission intensity exists, and stricter security changes the preferred operating point.

  • Existence condition: Positive secrecy transmission capacity is characterized by a condition involving the connection-outage and secrecy-outage constraints.The condition is also described through the average number of eavesdroppers within distance r of the transmitter.
  • QoS–security trade-off: The condition creates a QoS–security trade-off: achieving higher security requires accepting a larger connection-outage probability.Thus, a moderate connection outage probability is usually desirable for highly secure networks.
  • Transmission intensity: The feasibility condition does not depend on the spatial transmission intensity λ_l.Changing the number of active legitimate users alone cannot produce positive secrecy transmission capacity when the QoS and secrecy constraints are infeasible.
  • Optimal transmission intensity: Once feasibility holds, an optimal spatial transmission intensity λ_l exists and can be found numerically by maximizing the secrecy transmission capacity.In the low-capacity regime, the optimal value is given analytically and increases as the required security level increases.
  • Optimal transmission intensity: For highly secure networks, the optimal spatial transmission intensity is usually much higher than the eavesdropper density.The reported example uses ϵ = 0.01 and α = 4.

B. Optimal Connection Outage Probability in Sparse Networks

In sparse, interference-limited networks, the paper derives a closed-form connection-outage probability that maximizes secrecy transmission capacity. The optimum increases when a higher security level is required.

  • Sparse-network optimum: A closed-form solution for the optimal connection-outage probability is presented for sparse networks with λ_lπr^2 ≪ 1.The solution is obtained from the secrecy transmission-capacity expression by differentiating with respect to σ.
  • Assumptions: The analysis assumes an interference-limited network, where receiver noise is much weaker than aggregate interference.The path-loss exponent is also assumed not to be close to 2.
  • Sparse-network optimum: The optimal connection-outage probability maximizes the secrecy transmission capacity in the sparse-network regime.The closed-form expression uses the real-valued principal branch of Lambert’s W function.
  • Security dependence: The optimal connection-outage probability increases when a higher security level is required, corresponding to a lower secrecy-outage target ϵ.The analysis also notes that σ should not be chosen very close to 0.

IV. SECRECY GUARD ZONE

The secrecy guard-zone approach improves secure transmission by monitoring a finite disk around each legitimate transmitter. The paper compares silent non-cooperative transmitters with cooperative artificial-noise transmission.

  • Assumptions: The guard-zone analysis assumes legitimate transmitters can detect eavesdroppers within the relevant finite range.The secrecy transmission capacity is evaluated separately for each transmission protocol.
  • Guard-zone model: A secrecy guard zone is modeled as a disk of radius D centered at each legitimate transmitter.Confidential transmission occurs only when no eavesdropper is inside the disk.
  • Guard-zone model: Each transmitter independently decides whether to transmit based on whether its own secrecy guard zone contains eavesdroppers.This preserves the decentralized nature of the network.
  • Transmission protocols: The paper studies secrecy transmission capacity under two protocols: non-cooperative transmitters remain silent, whereas cooperative transmitters generate artificial noise.Both behaviors are triggered when eavesdroppers are detected inside the guard zone.

A. Secrecy Guard Zone with Non-Cooperative Transmitters

For non-cooperative transmitters, guard zones alter the active-transmitter and eavesdropper processes, so the paper derives outage expressions and computes secrecy transmission capacity numerically.

  • Point-process model: With non-cooperative transmitters, actual transmitters outside the guard zone are approximated as a homogeneous PPP from a typical receiver’s viewpoint.The paper notes that the actual transmitter process is generally non-homogeneous after introducing guard zones.
  • Connection outage: The connection-outage constraint P_co = σ determines the transmission rate R_t through β_t = 2R_t − 1.Connection outage excludes the event that transmission is suppressed because an eavesdropper lies inside the guard zone.
  • Secrecy outage: From a typical transmitter, eavesdroppers form a homogeneous PPP with density λ_e outside the transmitter’s secrecy guard zone.The secrecy-outage bound uses the eavesdropper process and Jensen’s inequality.
  • Secrecy outage: The secrecy-outage expression includes the probability that no eavesdropper lies inside the secrecy guard zone and the Laplace transform of interference.The interference is represented as a sum of received powers from actual transmitters.
  • Approximation caveat: A noted approximation can underestimate interference because interferers near the typical active transmitter are more likely to be active than distant interferers.This caveat concerns the second approximation used in the guard-zone analysis.
  • Capacity evaluation: The secrecy transmission capacity is obtained after substituting the secrecy-outage bound, with the relevant rate solved numerically under the secrecy-outage constraint.The model incorporates transmission probability through the density of actual transmitters.

B. Secrecy Guard Zone with Cooperative Transmitters

The cooperative secrecy-guard-zone protocol uses artificial noise from transmitters near eavesdroppers while preserving distributed operation. The resulting lower bound identifies when positive secrecy transmission capacity is possible and how guard-zone design affects throughput.

  • Protocol: Transmitters cooperate distributively by generating artificial noise when eavesdroppers lie inside the secrecy guard zone, without requiring coordination.The artificial noise is statistically identical to confidential messages and therefore cannot be distinguished by eavesdroppers.
  • Network model: The interferer set remains Φl with density λl, whereas the actual transmitter set is Φl′ with density λ′ under the guard-zone protocol.Because interferers remain as in the no-guard-zone case, the connection-outage probability and transmission rate retain their earlier forms.
  • Capacity analysis: A lower bound on secrecy transmission capacity is derived for cooperative transmitters operating with secrecy guard zones.The secrecy-outage bound is obtained from the eavesdropper PPP generating functional together with Jensen’s inequality.
  • Capacity analysis: Positive secrecy transmission capacity is determined by solving the lower-bound expression τ LB(r) > 0.The condition depends on the connection-outage constraint and guard-zone design parameters.
  • Design implications: The guard-zone improvement over the no-guard-zone case is [1 1−σ](D/r)2, while legitimate-transmitter density does not determine whether capacity is positive for fixed constraints.Positive capacity can instead be achieved by choosing σ and/or D to satisfy the derived condition.
  • Design implications: For fixed r, the minimum required D increases as σ or ϵ decreases below a threshold, and the optimal D is expected to increase similarly.Combining secrecy guard zones with CSMA or receiver-side interference guard zones is proposed as a future throughput improvement.

V. NUMERICAL RESULTS AND DISCUSSION

Numerical results quantify how security, outage constraints, node densities, guard zones, and cooperation shape secrecy transmission capacity. Moderate security incurs relatively little throughput cost, whereas stringent security sharply reduces throughput; guard zones and cooperation provide substantial benefits.

  • Security-throughput trade-off: The throughput cost of moderate security is relatively low, but strengthening security sharply increases the cost.At λ_l = 0.01, improving security from ϵ = 0.02 to ϵ = 0.01 reduces τ^LB(r) by 84%.
  • Guard zones and cooperation: A secrecy guard zone substantially improves secrecy transmission capacity under high security requirements.At ϵ = 0.01, capacity increases from 0.003 with D = 0 to 0.018 with a non-cooperative protocol and 0.021 with a cooperative protocol at D = 3.
  • Guard zones and cooperation: Guard zones enlarge the feasible ranges of connection and secrecy outage probabilities, although their benefit diminishes as security requirements relax.The optimal guard-zone radius decreases as acceptable secrecy outage, connection outage, or legitimate-node density increases, reaching zero at moderate-to-high ϵ.
  • Guard-zone optimization: The guard-zone benefit is observed for transmitter-receiver distances both below and above the guard-zone radius.The numerical illustration uses r = 1, but the reported benefit also appears for other values of r.
  • Guard zones and cooperation: Cooperative transmission outperforms non-cooperative transmission, with the largest difference occurring in networks requiring high security.At ϵ = 0.01, cooperation increases τ^LB(r) by 17% when D = 3 and 14% when D = 6.
  • Guard-zone optimization: Increasing legitimate-node interference permits a smaller guard zone while maintaining the same eavesdropper SIR, thereby increasing message-transmission intensity.The paper also reports significant improvement from small guard zones, including when the optimal radius lies within transmitters’ maximum detection range.

VI. CONCLUSIONS

The paper defines secrecy transmission capacity to study secure throughput in large-scale decentralized wireless networks using stochastic-geometry tools. It finds that moderate security has a relatively low throughput cost, whereas highly secure operation is expensive; secrecy guard zones with artificial noise can reduce that cost.

  • Conclusions: The secrecy transmission capacity measures secure network throughput and can be characterized analytically for Rayleigh fading channels.The analysis uses transmission-capacity tools and existing stochastic-geometry results.
  • Conclusions: Moderate security causes a relatively small throughput reduction, but achieving highly secure networks becomes very expensive.The reduction in secrecy transmission capacity as the security requirement tightens represents the throughput cost of improving physical-layer security.
  • Conclusions: Secrecy guard zones with artificial noise can dramatically reduce the throughput cost of achieving highly secure networks.The paper presents guard zones as a simple technique for improving throughput under stringent security requirements.
  • Conclusions: The model can be extended to other transmission techniques, medium access-control protocols, and eavesdropping strategies.These extensions are identified as directions for future work.
  • Conclusions: The current model assumes homogeneous Poisson-distributed nodes and considers only single-hop transmissions.End-to-end throughput analysis for multi-hop wireless networks with physical-layer security remains an open problem, while the effect of eavesdropper distribution also remains to be studied.
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