PaperlayerView exact revision on arXiv

Source-linked AI summary

Artificial Noise Aided Secure Cognitive Beamforming for Cooperative MISO-NOMA Using SWIPT

Fuhui Zhou, Zheng Chu, Haijian Sun, Rose Qingyang Hu, Lajos Hanzo

arXiv:1802.09609v1eess.SPcs.GT

TL;DR

The paper tackles secure, energy-aware transmission in MISO-NOMA cognitive radio networks using SWIPT, where eavesdropping, non-linear harvesting, interference, and CSI uncertainty must be handled together. It jointly designs artificial-noise cooperation and beamforming under perfect and bounded-error CSI, finding that cooperative jamming improves security, NOMA outperforms OMA in power efficiency, and the cost-function algorithm surpasses SDR.

  • Problem

    Existing secure NOMA and cognitive-radio resource-allocation schemes do not jointly address NOMA, SWIPT energy-harvesting requirements, cross-network interference, multiple malicious receivers, and imperfect CSI.

  • Method

    The paper jointly optimizes primary and secondary beamforming vectors and the secondary transmitter’s artificial-noise covariance to minimize total power under secrecy-rate and energy-harvesting constraints.

  • Results

    NOMA achieves better performance than OMA, the cooperative jamming scheme improves secure communications, and the cost-function algorithm outperforms the SDR-based algorithm.

  • Takeaways & Limitations

    Artificial-noise cooperation is effective for improving security in MISO-NOMA cognitive radio networks using SWIPT, while the cost-function approach provides the stronger algorithmic result.

Abstract

from arXiv · show

Cognitive radio (CR) and non-orthogonal multiple access (NOMA) have been deemed two promising technologies due to their potential to achieve high spectral efficiency and massive connectivity. This paper studies a multiple-input single-output NOMA CR network relying on simultaneous wireless information and power transfer (SWIPT) conceived for supporting a massive population of power limited battery-driven devices. In contrast to most of the existing works, which use an ideally linear energy harvesting model, this study applies a more practical non-linear energy harvesting model. In order to improve the security of the primary network, an artificial-noise-aided cooperative jamming scheme is proposed. The artificial-noise-aided beamforming design problems are investigated subject to the practical secrecy rate and energy harvesting constraints. Specifically, the transmission power minimization problems are formulated under both perfect channel state information (CSI) and the bounded CSI error model. The problems formulated are non-convex, hence they are challenging to solve. A pair of algorithms either using semidefinite relaxation (SDR) or a cost function are proposed for solving these problems. Our simulation results show that the proposed cooperative jamming scheme succeeds in establishing secure communications and NOMA is capable of outperforming the conventional orthogonal multiple access in terms of its power efficiency. Finally, we demonstrate that the cost function algorithm outperforms the SDR-based algorithm.

I. INTRODUCTION

The paper addresses secure communications in MISO-NOMA cognitive radio networks using SWIPT, where eavesdropping, practical energy harvesting, CSI uncertainty, and cross-network interference must be considered. It proposes artificial-noise-aided cooperation and jointly optimized beamforming designs for these settings.

  • Motivation: SWIPT-enabled cognitive radio networks are vulnerable to eavesdropping because malicious energy-harvesting receivers may intercept confidential transmissions.Physical-layer security is therefore considered for protecting both primary and secondary communications.
  • Research gap: Prior secure-resource-allocation studies largely addressed conventional OMA or NOMA systems separately and often assumed perfect CSI.These schemes do not directly account for the interference and energy-harvesting requirements of NOMA cognitive radio networks using SWIPT.
  • Scope: The paper studies MISO-NOMA cognitive radio networks using SWIPT with multiple malicious energy-harvesting receivers and a practical non-linear energy-harvesting model.Both perfect CSI and bounded CSI error models are considered.
  • Proposed approach: An artificial-noise-aided cooperative scheme lets the secondary base station jam malicious receivers while gaining access to primary-network frequency bands.The scheme jointly optimizes the jamming covariance matrix and the primary and secondary beamforming vectors.
  • Optimization: The total transmission power is minimized subject to secrecy-rate and energy-harvesting constraints under the considered CSI models.The resulting beamforming design problems are addressed with algorithms based on semidefinite relaxation or a cost function.

C. Organization and Notations

The paper defines the organization, notation, and network setting for downlink MISO-NOMA cognitive radio networks using SWIPT. The primary and secondary networks share spectrum, while artificial-noise cooperation supports security and energy transfer.

  • Organization: The paper presents the system model, secure beamforming problems under perfect and bounded-error CSI, simulations, and conclusions across Sections II–VI.Section II covers the network model, Section III perfect CSI, Section IV bounded CSI error, and Section V simulations.
  • Notation: The notation defines vectors and matrices, Hermitian transpose, trace, rank, positive semidefiniteness, vectorization, norms, eigenvalues, and complex Gaussian distributions.These conventions support the beamforming and covariance-matrix formulations used throughout the paper.
  • Network model: The primary network uses unicast-multicast transmission, while the secondary base station provides SWIPT to secondary users and energy-harvesting receivers using NOMA.Primary and secondary networks coexist through spectrum sharing.
  • Threat model: Energy-harvesting receivers can intercept confidential information because NOMA broadcasts signals and SWIPT RF signals serve dual information-and-energy functions.The model assumes each network’s energy-harvesting receivers intercept only information from that same network.
  • Cooperation and CSI: The cooperative scheme has the secondary base station transmit jamming to protect primary users, in exchange for secondary access to the primary network’s frequency bands.Both perfect and imperfect CSI cases are studied, with perfect CSI serving as a performance bound.

B. Security Metrics

The security-metric model specifies received signals, confidential information-bearing beamformers, artificial-noise covariance matrices, and secrecy rates for users and energy-harvesting receivers. A conservative decoding assumption is used to represent worst-case secondary-user interception.

  • Received signals: The model defines received signals separately for primary users, secondary users, and energy-harvesting receivers in both networks.These signals are indexed by cluster, user, and energy-harvesting-receiver identifiers.
  • Channels and beamforming: The channel vectors describe links from the primary and secondary base stations to legitimate users and energy-harvesting receivers.The beamforming and interception expressions use these channel vectors to characterize received signals and security metrics.
  • Signal construction: Primary and secondary confidential messages use beamforming vectors, while artificial noise is generated at the primary and secondary transmitters.The artificial-noise vectors follow complex Gaussian distributions with covariance matrices Σp,m and Σs.
  • Secrecy metrics: The secrecy rates Rp,m,i and Rs,j quantify confidential-transmission security for primary and secondary users, respectively.Their associated signal and interception terms are defined through the system’s received-signal expressions.
  • Worst-case interception: The secondary-network energy-harvesting receiver is assumed to decode user j’s message before user i’s message, j < i, producing a worst-case secrecy-rate model.The paper identifies this as an overestimate of the receiver’s interception capability.

C. Non-linear Energy Harvesting Model

The paper uses a practical non-linear energy-harvesting model instead of an ideally linear model. Harvested power depends on circuit parameters, received RF power, and saturation limits for receivers in both networks.

  • Model scope: The harvesting-power model is applied to energy-harvesting receivers in the primary and secondary networks.The receiver set is A = A1 ∪ A2, with A1 covering primary-network receivers and A2 covering the secondary-network receiver set.
  • Circuit dependence: The non-linear model includes parameters ae,A and be,A that reflect energy-harvesting circuit specifications.The cited specifications include resistance, capacitance, and diode turn-on voltage.
  • Saturation: P max e,A represents the maximum harvested power when the energy-harvesting circuit is saturated.This saturation limit distinguishes the model from an unbounded linear harvesting relationship.
  • Received power: The received RF power Γe,A is assigned according to whether the energy-harvesting receiver belongs to the primary or secondary network.Noise power is ignored because it is small compared with RF signal power.
  • Optimization: Under perfect CSI, the total transmission power is minimized while secrecy-rate and harvested-power requirements are enforced.The corresponding artificial-noise-aided beamforming design is non-convex and is addressed with suboptimal schemes.

A. AN-aided Beamforming Design Problem

The design jointly minimizes PBS and CBS transmission power while satisfying secrecy-rate and energy-harvesting requirements. The resulting problem is non-convex because of secrecy and rank-one beamforming constraints.

  • The beamforming weights and artificial-noise covariances of the PBS and CBS are jointly optimized to minimize total transmission power.The optimization covers both base stations under secrecy-rate and energy-harvesting constraints.
  • The formulation enforces minimum secrecy rates for PUs and SUs and minimum harvested-energy requirements for primary and secondary EHRs.The secrecy thresholds are represented by γp,m,i and γs,j, while EH thresholds are represented by ζe,A1 and ζe,A2.
  • P1 is non-convex and difficult to solve because it includes secrecy-rate constraints and the rank-one constraint required for rank-one beamforming.The rank-one constraint is denoted C5, while C1 and C2 enforce PU and SU secrecy rates.

B. Suboptimal Solution Based on SDR

The SDR-based approach introduces auxiliary variables and successive convex approximations to transform the original problem into iteratively solvable convex subproblems. It may require Gaussian randomization when the relaxed beamforming matrices are not rank-one.

  • An auxiliary variable τm is introduced to express the PU secrecy-rate constraint equivalently.
  • Successive convex approximation replaces the non-convex PU and SU secrecy constraints with tractable approximations using auxiliary and approximate variables.The approximations become equal to the corresponding variables when the constraints are tight.
  • Using SDR, the problem is converted into convex problem P2, which can be efficiently solved with CVX at each iteration.Algorithm 1 calculates the solution of the original problem through these iterative convex solves.
  • If the relaxed beamforming matrices are not rank-one, Gaussian randomization produces suboptimal beamforming vectors instead of guaranteed optimal weights.Rank-one matrices yield optimal beamforming vectors through eigenvalue decomposition.

C. Suboptimal Solution Based on Cost Function

The cost-function approach incorporates rank-one enforcement into the SDR formulation using a penalty factor and linearizes the resulting non-convex eigenvalue terms. Iterative convex problems then produce a solution to the original design.

  • The rank-one constraints are incorporated into a cost function, reformulating P2 as P3 with a positive cost factor ℓ.
  • Because maximum-eigenvalue terms are convex, P3 remains non-convex and is addressed using a supporting inequality from Lemma 1.The lemma lower-bounds the difference of maximum eigenvalues using an eigenvector associated with the maximum eigenvalue.
  • Using Lemma 1, P3 is approximated by convex problem P4 for iterative solution.P4 can be solved using CVX, enabling Algorithm 2 to solve P1 iteratively.
  • The iterative objective includes a penalty based on the gap between each matrix's trace and maximum eigenvalue to promote rank-one solutions.The iteration index is denoted by n in the cost-function formulation.

IV. AN-AIDED BEAMFORMING DESIGN UNDER IMPERFECT CSI

Under imperfect CSI, the beamforming design addresses bounded channel-estimation errors caused by limited cooperation between the primary and secondary networks. The cost-function-based algorithm is presented for this setting.

  • The CSI between the CBS and primary-network EHRs and between the PBS and secondary-network EHRs is modeled as imperfect.
  • The cost function-based algorithm is listed for the imperfect-CSI beamforming design problem.
  • The paper adopts a bounded CSI error model to represent channel-estimation errors arising from limited cooperation between the networks.Other CSI links can be obtained through cooperation between the primary and secondary networks.

A. Robust AN-aided Beamforming Design Problem Formulation

The robust design models channel uncertainty with bounded error regions and formulates transmission-power minimization under secrecy-rate and harvested-power constraints. The resulting problem is difficult because uncertainty creates infinitely many inequalities and constraints C6–C10 are non-convex.

  • The bounded-error model represents each channel as an estimate plus an estimation error within a specified uncertainty region.The uncertainty regions are characterized by radii for the corresponding channel vectors.
  • The robust optimization minimizes transmission power while enforcing secrecy-rate constraints for primary and secondary users and harvested-power requirements for energy-harvesting receivers.
  • Infinite inequality constraints arise from the uncertain channel regions, while constraints C6–C10 introduce additional non-convexity.

B. Suboptimal Solution Based on Cost Function

The cost-function solution makes the robust problem tractable by applying the S-Procedure and successive convex approximation, then solving a sequence of convex subproblems. Slack and auxiliary variables support the approximations, and CVX solves each convex problem iteratively.

  • The S-Procedure is applied to convert the robust problem with uncertain channel regions into a tractable form.
  • Successive convex approximation transforms constraints C6–C9 using slack and auxiliary variables before the iterative optimization procedure.The approximations introduce nonnegative slack variables and auxiliary variables for the secrecy-rate and related constraints.
  • The resulting problem P6 is convex and can be solved with CVX, while Algorithm 2 iteratively solves the original robust problem P5.

V. SIMULATION RESULTS

The simulations compare NOMA and TDMA, cooperative jamming, CSI assumptions, and two optimization algorithms using minimum transmission power, convergence, and rank-one solutions. Across these settings, cooperative jamming and NOMA reduce required power, while Algorithm 2 generally outperforms Algorithm 1 at higher computational complexity.

  • NOMA and cooperation: NOMA consumes less minimum transmission power than TDMA with and without cooperation between the primary and secondary networks.The comparison is made under the perfect CSI scenario as the number of EHRs varies.
  • NOMA and cooperation: Cooperative jamming lowers the minimum transmission power compared with transmission without cooperation and supports secure communications.The proposed scheme uses cooperation between the primary and secondary networks to improve the security of the PUs.
  • Rank-one solutions: Algorithm 2 outperforms Algorithm 1 because it obtains rank-one solutions, enabling optimal beamforming vectors for the CBS and PBS.Algorithm 1 does not provide rank-one solutions, whereas Algorithm 2 applies a cost function related to rank-one solutions.
  • Secrecy-rate comparison: The minimum transmission power increases with the secrecy rate requirement of PUs, while cooperative jamming requires less power than the no-cooperation case.These observations are reported for two EHRs in the secondary network under perfect CSI.
  • Algorithm comparison: Algorithm 2 requires more iterations than Algorithm 1 because its computational complexity is higher, indicating a complexity–power-minimization tradeoff.Both algorithms require only a few iterations to converge.
  • CSI robustness: Under bounded CSI errors, both algorithms consume more transmission power than under perfect CSI, while Algorithm 2 remains superior for power minimization.The higher power is attributed to guaranteeing PU and SU secrecy rates with imperfect CSI.

VI. CONCLUSIONS

The paper develops secure beamforming for MISO NOMA CRNs using SWIPT and a practical non-linear energy-harvesting model. It jointly optimizes transmission and artificial-noise strategies under perfect and bounded-error CSI, finding advantages for NOMA, cost-function optimization, and cooperative jamming.

  • The study applies a practical non-linear energy-harvesting model to secure MISO NOMA CRNs using SWIPT.
  • Beamforming vectors and the artificial-noise covariance matrix are jointly optimized to minimize total transmission power while satisfying secrecy-rate and energy-harvesting requirements.
  • The beamforming problems are examined under perfect CSI and a bounded CSI error model, with two algorithms proposed for the resulting non-convex problems.
  • NOMA outperforms OMA, the cost-function algorithm outperforms SDR, and cooperative jamming improves security in MISO NOMA CRNs using SWIPT.
Loading 1802.09609v1…