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Physical-Layer Security with Multiuser Scheduling in Cognitive Radio Networks

Yulong Zou, Xianbin Wang, Weiming Shen

arXiv:1311.0404v1cs.IT

TL;DR

The paper addresses secure cognitive transmissions when multiple eavesdroppers operate under a primary user’s QoS constraint. It proposes secrecy-rate-based multiuser scheduling, compares it with traditional scheduling and artificial noise, and analyzes secrecy rate, intercept probability, and diversity. The proposed scheme generally performs best in the reported comparisons and achieves full diversity.

  • Problem

    Physical-layer security in cognitive radio networks with multiple eavesdroppers is rarely investigated despite the vulnerability of their open, dynamic architecture.

  • Method

    The paper schedules the CU maximizing achievable secrecy rate while satisfying the primary QoS constraint, then analyzes it against traditional scheduling and artificial noise in Rayleigh fading.

  • Results

    The proposed scheduling generally outperforms traditional scheduling and artificial noise in achievable secrecy rate and intercept probability, and achieves full diversity.

  • Takeaways & Limitations

    Exploiting multiuser scheduling improves cognitive-transmission security, with increasing CU count reducing intercept probability for the proposed and traditional schemes.

Abstract

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In this paper, we consider a cognitive radio network that consists of one cognitive base station (CBS) and multiple cognitive users (CUs) in the presence of multiple eavesdroppers, where CUs transmit their data packets to CBS under a primary user's quality of service (QoS) constraint while the eavesdroppers attempt to intercept the cognitive transmissions from CUs to CBS. We investigate the physical-layer security against eavesdropping attacks in the cognitive radio network and propose the user scheduling scheme to achieve multiuser diversity for improving the security level of cognitive transmissions with a primary QoS constraint. Specifically, a cognitive user (CU) that satisfies the primary QoS requirement and maximizes the achievable secrecy rate of cognitive transmissions is scheduled to transmit its data packet. For the comparison purpose, we also examine the traditional multiuser scheduling and the artificial noise schemes. We analyze the achievable secrecy rate and intercept probability of the traditional and proposed multiuser scheduling schemes as well as the artificial noise scheme in Rayleigh fading environments. Numerical results show that given a primary QoS constraint, the proposed multiuser scheduling scheme generally outperforms the traditional multiuser scheduling and the artificial noise schemes in terms of the achievable secrecy rate and intercept probability. In addition, we derive the diversity order of the proposed multiuser scheduling scheme through an asymptotic intercept probability analysis and prove that the full diversity is obtained by using the proposed multiuser scheduling.

I. INTRODUCTION

The paper studies physical-layer security in underlay cognitive radio networks, where cognitive transmissions coexist with primary-user communication while multiple eavesdroppers attempt interception. It motivates multiuser scheduling under primary QoS protection and models the resulting system with mutual interference, Rayleigh fading, and global CSI.

  • Cognitive radio setting: Cognitive radio lets unlicensed users access licensed spectrum, either through detected spectrum holes or simultaneous access constrained by primary-user QoS.The paper focuses on the underlay paradigm, where primary and cognitive transmissions share the spectrum concurrently.
  • Security motivation: Physical-layer security is needed because cognitive radio’s open, dynamic architecture exposes transmissions to passive eavesdroppers.Unlike active attacks, eavesdroppers attempt to intercept legitimate signals without transmitting harmful detectable signals.
  • Paper objective: The paper proposes scheduling a CU that maximizes achievable secrecy rate under the primary QoS constraint and analyzes security against multiple eavesdroppers.It compares the proposed scheme with traditional scheduling and artificial noise, using achievable secrecy rate, intercept probability, and diversity order.
  • System model: The network contains one CBS, M CUs, and N eavesdroppers, with single-antenna nodes and main and wiretap links between cognitive users, CBS, and eavesdroppers.The primary network contains one PT and one PR; the cognitive network operates alongside it over the same band.
  • Primary QoS constraint: Underlay transmission requires interference received at the primary receiver to remain below the maximum tolerable level I, making each CU’s transmit power a random variable.The random transmit power creates additional challenges for secrecy-rate and intercept-probability analysis.

III. PROPOSED MULTIUSER SCHEDULING AND ACHIEVABLE SECRECY RATE ANALYSIS

The proposed scheme selects one cognitive user using both main-link and wiretap-link CSI while enforcing the primary QoS constraint. Its secrecy-rate analysis accounts for the strongest eavesdropper and uses numerical evaluation when a closed-form ergodic expression is unavailable.

  • Proposed scheduling: The proposed multiuser scheduling scheme selects one of M CUs for transmission to CBS while defending against eavesdropping attacks.The scheme is analyzed alongside traditional scheduling and artificial noise as benchmark approaches.
  • Wiretap-link analysis: The wiretap-link rate is the maximum individual eavesdropper rate because the N eavesdroppers independently attempt interception.The overall wiretap rate is therefore determined by the strongest eavesdropper.
  • Secrecy-rate criterion: Achievable secrecy rate is obtained as the nonnegative difference between the main-link capacity and the overall wiretap-link capacity.The scheduling criterion chooses the CU with the highest achievable secrecy rate.
  • CSI-aware selection: The proposed scheduler uses both main-link CSI and wiretap-link CSI when selecting the transmitting CU.This distinguishes it from traditional scheduling, which maximizes the desired-destination data rate without considering eavesdropping.
  • Ergodic analysis: The ergodic secrecy rate is numerically determined because obtaining a closed-form solution to the high-dimensional integral is challenging.The analysis assumes positive variables xi, yi, and zij in the resulting integral.

B. Traditional Multiuser Scheduling Scheme

Traditional multiuser scheduling is used as a benchmark that selects the CU maximizing CBS’s achievable data rate without accounting for eavesdropping. Its secrecy rate is then evaluated against the strongest eavesdropper.

  • Traditional scheduling criterion: Traditional scheduling selects the CU with the highest achievable rate at CBS among the M cognitive users.Its objective does not explicitly consider eavesdropping attacks.
  • Main-link rate: The traditional scheme’s overall CBS rate is calculated for the CU selected by its data-rate-based criterion.The selected user is denoted by o in the subsequent analysis.
  • Secrecy-rate analysis: The traditional scheme’s secrecy rate combines the selected CU’s CBS rate with the maximum rate achieved by the eavesdroppers.Its ergodic secrecy rate is subsequently obtained from the secrecy-rate expression.

C. Conventional Artificial Noise Scheme

The artificial noise benchmark has cognitive users transmit desired signals and coordinated interference intended to degrade eavesdroppers without affecting CBS. Its secrecy rate is analyzed under equal power allocation and evaluated numerically.

  • Artificial-noise principle: The artificial noise scheme generates interfering signals designed to affect eavesdroppers while leaving the intended CBS unaffected.The scheme is included as a conventional physical-layer security benchmark.
  • Power allocation: Artificial-noise transmission allocates power between desired signals and artificial noise while constraining total interference at the primary receiver.Equal allocation limits each CU’s interference contribution to I/M when M CUs transmit simultaneously.
  • Interference design: The artificial-noise vector is designed to satisfy h_ib w_i = 0 so that artificial noise does not interfere with CBS.The requirement can be satisfied when the number of CUs is at least two.
  • Secrecy-rate formulation: The artificial-noise secrecy rate is formed from the CBS rate and the highest eavesdropper rate after artificial-noise interference is applied.The eavesdroppers’ overall rate is the highest among their individual rates.
  • Numerical evaluation: The artificial-noise ergodic secrecy rate is evaluated through computer simulations because its closed-form averaging is challenging and cumbersome.The simulations compare it with single-user transmission and both multiuser scheduling schemes.

D. Numerical Secrecy Rate Results

The numerical results compare achievable secrecy rates across scheduling and artificial-noise schemes as MER, eavesdropper count, and CU count vary. The proposed scheduling generally outperforms traditional scheduling, while artificial noise is strongest at low MER and can lose its advantage at higher MER.

  • At low MER, artificial noise outperforms both traditional and proposed multiuser scheduling, but scheduling schemes become superior beyond a critical MER.The artificial-noise advantage reverses because it consumes power that could otherwise support secrecy transmission.
  • For N = 2 and N = 8, the proposed multiuser scheduling scheme always achieves a higher secrecy rate than traditional multiuser scheduling.
  • As eavesdroppers increase from N = 2 to N = 8, traditional and proposed scheduling secrecy rates decrease significantly, whereas artificial-noise secrecy rate decreases non-significantly.Artificial noise remains more robust to eavesdroppers’ channel conditions because it generates interference against eavesdropping attacks.
  • As CUs increase from M = 2 to M = 8, the secrecy rates of both traditional and proposed multiuser scheduling increase significantly.Traditional scheduling remains below proposed scheduling while still benefiting from additional CUs.
  • When eavesdroppers’ CSI is unavailable, traditional scheduling still enhances security; when it is available, proposed scheduling is the better choice.

IV. INTERCEPT PROBABILITY ANALYSIS OVER RAYLEIGH FADING CHANNELS

The paper analyzes intercept probability for traditional and proposed multiuser scheduling and artificial noise over Rayleigh fading channels. For proposed scheduling, the analysis uses independent exponential channel gains and derives a closed-form intercept-probability expression.

  • The intercept-probability analysis covers traditional and proposed multiuser scheduling and artificial noise over Rayleigh fading channels.
  • For proposed scheduling, an intercept event occurs when the main-link achievable secrecy rate is less than the wiretap-link secrecy rate.
  • The proposed-scheduling derivation models |h_ib|^2, |h_ip|^2, and |h_iej|^2 as independent exponentially distributed random variables.
  • Using the binomial theorem, eavesdropper subsets, and integration, the paper obtains a closed-form intercept-probability expression for proposed multiuser scheduling.
  • MER denotes the main-to-eavesdropper ratio throughout the paper.

B. Traditional Multiuser Scheduling Scheme

The traditional scheduling analysis derives intercept probability from the secrecy-rate expressions. A general closed form is difficult, so the paper illustrates the result numerically and analytically for the single-CU case.

  • The traditional-scheduling intercept probability is formulated from Eqs. (12) and (13) and then simplified.
  • A general closed-form solution for arbitrary M and N is difficult to obtain, so numerical intercept probabilities can be determined through computer simulations.
  • For M = 1, the analysis substitutes a single CU into the general expression and uses exponential channel distributions and independence assumptions.The derivation applies the binomial expansion formula over non-empty eavesdropper subsets.

C. Conventional Artificial Noise Scheme

The analysis compares artificial noise with traditional and proposed multiuser scheduling using intercept probability, finding the proposed scheme performs best under the illustrated settings. Increasing the number of cognitive users further reduces intercept probability for both scheduling schemes.

  • Analytical intercept probability: The artificial-noise analysis derives its intercept probability, an upper bound, and a special-case comparison with traditional scheduling for M = 1.For M = 1, the artificial noise scheme has strictly lower intercept probability than traditional user scheduling.
  • Comparison with competing schemes: The proposed multiuser scheduling scheme has lower intercept probability than both traditional scheduling and artificial noise in Fig. 5.The comparison uses M = N = 4 and I = Nb = Nej = 0dBm.
  • Effect of the number of CUs: For M = 4, M = 6, and M = 8, proposed scheduling significantly outperforms traditional scheduling in intercept probability, especially at high MER.Fig. 6 compares the two scheduling schemes with N = 4.
  • Effect of the number of CUs: Increasing the number of CUs from M = 4 to M = 8 significantly reduces intercept probabilities for both proposed and traditional scheduling.The result identifies multiuser scheduling as providing security benefits against eavesdropping attacks.

V. DIVERSITY ORDER ANALYSIS

The paper defines security diversity through the asymptotic relationship between intercept probability and MER, then analyzes the proposed scheduling scheme under multiple eavesdroppers. The resulting diversity order equals the number of CUs, establishing full diversity, while eavesdropper count affects performance but not the asymptotic decay rate.

  • Security diversity definition: Security diversity is defined from the asymptotic ratio of logarithmic intercept probability to logarithmic MER because intercept probability is independent of signal power.The traditional BER-based diversity definition is therefore inapplicable in this cognitive transmission setting.
  • Asymptotic analysis: The proposed scheduling analysis models eavesdropper channel gains as independent exponential variables and derives their CDF and PDF using non-empty eavesdropper subsets.These distributions support the subsequent asymptotic intercept probability analysis.
  • Asymptotic analysis: The asymptotic intercept probability expression is obtained by substituting prior expansions and ignoring high-order infinitesimals as λ_me →∞.The derivation uses the relevant expressions for the proposed scheduling scheme and its intercept probability.
  • Diversity-order result: d = M, so the diversity order equals the number of CUs and the proposed multiuser scheduling scheme achieves full diversity.This is the principal asymptotic result of the section.
  • Diversity-order result: Increasing the number of eavesdroppers degrades intercept probability but does not change the speed of its decrease as λ_me →∞.By contrast, increasing the number of CUs makes the asymptotic intercept-probability curve steeper.

VI. CONCLUSION

The proposed multiuser scheduling scheme improves cognitive transmission security under a primary QoS constraint and achieves full diversity. Its secrecy-rate advantage depends on the MER region, while user fairness remains unaddressed.

  • The proposed multiuser scheduling scheme always achieves a higher achievable secrecy rate than traditional multiuser scheduling.
  • Beyond a critical MER value, both scheduling schemes achieve higher achievable secrecy rates than artificial noise.In the low MER region, both scheduling schemes have smaller achievable secrecy rates than artificial noise under the primary QoS constraint.
  • Full diversity is achieved by the proposed multiuser scheduling scheme through asymptotic intercept probability analysis.This result demonstrates the security benefit of exploiting multiuser scheduling against eavesdropping attacks.
  • User fairness is not considered, so users experiencing severe propagation loss may be rarely scheduled and face long channel access delays.The paper identifies QoS-guaranteed fair scheduling as a direction for future work.

APPENDIX A PROOF OF EQ. (45)

Appendix A proves Eq. (45) by analyzing the asymptotic behavior of auxiliary random-variable moments as λ_me tends to infinity. The derivation then applies a Taylor expansion and substitutions to complete the result.

  • The proof shows that E(t) and E(t^2) approach zero as λ_me →∞.Consequently, t approaches zero with probability one in this limit.
  • With t →0 almost surely, the proof uses a Taylor series expansion to derive the asymptotic expression.
  • The resulting expression leads to Eq. (45), completing the proof.The appendix obtains the result through successive substitutions into the preceding equations.
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