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Secrecy Transmit Beamforming for Heterogeneous Networks

Tiejun Lv, Hui Gao, Shaoshi Yang

arXiv:1503.01056v1cs.IT

TL;DR

The paper studies physical-layer security for a two-tier downlink HetNet in which an eavesdropper targets a legitimate macrocell user. It proposes macrocell-only, sequential cooperative, and jointly designed secrecy beamforming schemes with tractable SOCP and SDP reformulations. The simulations demonstrate improved secrecy-rate performance for the proposed schemes.

  • Problem

    Physical-layer security is studied in a two-tier HetNet where an eavesdropper wiretaps a legitimate macrocell user amid macrocell–femtocell interference.

  • Method

    The paper proposes STB-OM under OSA, STB-SMF under SONOSA with sequential FBS cooperation, and STB-JMF with joint MBS–FBS beamforming, using SOCP and SDP reformulations.

  • Results

    Simulation results show the effectiveness of the three proposed secrecy transmit beamforming schemes in improving HetNet secrecy-rate performance.

  • Takeaways & Limitations

    Spectrum allocation and cooperation can be combined with secrecy transmit beamforming to exploit HetNet interference for secure communication while accounting for legitimate-user QoS.

Abstract

from arXiv · show

In this paper, we pioneer the study of physical-layer security in heterogeneous networks (HetNets). We investigate secure communications in a two-tier downlink HetNet, which comprises one macrocell and several femtocells. Each cell has multiple users and an eavesdropper attempts to wiretap the intended macrocell user. Firstly, we consider an orthogonal spectrum allocation strategy to eliminate co-channel interference, and propose the secrecy transmit beamforming only operating in the macrocell (STB-OM) as a partial solution for secure communication in HetNet. Next, we consider a secrecy-oriented non-orthogonal spectrum allocation strategy and propose two cooperative STBs which rely on the collaboration amongst the macrocell base station (MBS) and the adjacent femtocell base stations (FBSs). Our first cooperative STB is the STB sequentially operating in the macrocell and femtocells (STB-SMF), where the cooperative FBSs individually design their STB matrices and then feed their performance metrics to the MBS for guiding the STB in the macrocell. Aiming to improve the performance of STB-SMF, we further propose the STB jointly designed in the macrocell and femtocells (STB-JMF), where all cooperative FBSs feed channel state information to the MBS for designing the joint STB. Unlike conventional STBs conceived for broadcasting or interference channels, the three proposed STB schemes all entail relatively sophisticated optimizations due to QoS constraints of the legitimate users. In order to efficiently use these STB schemes, the original optimization problems are reformulated and convex optimization techniques, such as second-order cone programming and semidefinite programming, are invoked to obtain the optimal solutions. Numerical results demonstrate that the proposed STB schemes are highly effective in improving the secrecy rate performance of HetNet.

I. INTRODUCTION

The paper addresses physical-layer security in two-tier HetNets by using spectrum allocation, cooperative beamforming, and tractable reformulations to improve secrecy while respecting legitimate-user QoS.

  • Motivation: Physical-layer security is motivated by growing wireless demands and the limitations of relying solely on computationally secure key-based protection.The paper places physical-layer security within broader efforts to improve coverage, data rate, and reliable secrecy in dense heterogeneous networks.
  • Motivation: Deliberately generated co-channel interference can improve secrecy, motivating dynamic spectrum allocation and cooperation between macrocell and femtocell base stations.The proposed direction treats interference as a resource that can be arranged to hinder the eavesdropper.
  • Contributions: The paper studies a two-tier downlink HetNet where an eavesdropper wiretaps a legitimate macrocell user, using OSA for STB-OM and SONOSA for cooperative STB schemes.STB-OM requires no MBS–FBS cooperation, while the cooperative schemes exploit adjacent FBSs.
  • Contributions: STB-SMF has cooperative FBSs independently design beamforming to interfere with the eavesdropper, then send performance metrics to the MBS for macrocell design.The scheme preserves QoS for the relevant legitimate users while introducing secrecy-oriented cooperation.
  • Contributions: STB-JMF sends cooperative FBS channel state information to the MBS for joint beamforming that balances secrecy-rate enhancement with MU and FU QoS constraints.The paper presents this as an improvement over the sequential cooperative design.
  • Optimization: The nonconvex designs are reformulated using SOCP and SDP techniques, with the STB-OM formulation using iterative first-order Taylor approximations.The iterative approximation improves at each iteration and yields a local optimum for the original STB-OM problem.

II. SYSTEM MODEL

The system model contains a macrocell, multiple femtocells, legitimate users, and an eavesdropper, with OSA eliminating cross-tier interference and SONOSA selectively creating cooperative interference.

  • Network model: The HetNet comprises an NM-antenna MBS serving M single-antenna MUs, an eavesdropper targeting MU1, and FBSs serving K single-antenna FUs.The model assumes NM > M and NF > K, with FBS locations distributed according to a homogeneous Poisson point process.
  • Spectrum allocation: OSA assigns orthogonal resources to the MBS and adjacent FBSs, eliminating cross-tier and adjacent-femtocell interference, whereas SONOSA changes this local allocation to enable cooperation.Under SONOSA, FBSs adjacent to the eavesdropper share the MBS frequency resource.
  • Spectrum allocation: SONOSA uses N cooperative FBSs to generate co-channel interference against the eavesdropper while serving their own femtocell users.The cooperative FBSs are selected from the FBSs using the shared macrocell frequency resource.
  • Signal model: The model defines received signals and SINRs for macrocell users, the eavesdropper, and femtocell users, together with transmit-power constraints for MBS and FBS precoders.Channel vectors connect the MBS and FBSs to their respective legitimate users and to the eavesdropper.
  • Assumptions and scope: The analysis assumes perfect CSI and focuses on beamforming design; identifying which MU has been intercepted is left for future work.The paper states that imperfect-CSI models and the identification problem are future directions.

III. SECURITY TRANSMIT BEAMFORMING SCHEMES FOR HETNET

The paper combines spectrum allocation with transmit beamforming in three secrecy schemes, progressing from macrocell-only design to sequential and joint MBS–FBS cooperation.

  • III. SECURITY TRANSMIT BEAMFORMING SCHEMES FOR HETNET: Three schemes are proposed: STB-OM under OSA, STB-SMF under SONOSA with sequential cooperation, and STB-JMF under SONOSA with joint cooperation.Their designs differ in how strongly the MBS and cooperative FBSs collaborate while improving the secrecy rate of the intended MU.

A. Secrecy Transmit Beamforming Only Performed in Macrocell (STB-OM)

STB-OM maximizes the secrecy rate of one macrocell user under OSA while satisfying legitimate-user QoS constraints. Its nonconvex optimization is iteratively approximated and solved through convex SOCP subproblems.

  • STB-OM formulation: STB-OM maximizes MU1's secrecy rate while guaranteeing the SINR requirements of other legitimate macrocell users under OSA.OSA assigns orthogonal frequency resources to the MBS and FBSs, eliminating co-channel interference.
  • STB-OM optimization: First-order Taylor approximations transform the nonconvex formulation into a convex SOCP that is repeatedly solved and updated until convergence.The approximation is refined at each iteration, and the resulting convex subproblem can be solved with standard solvers.
  • STB-OM optimization: The original STB-OM problem is nonconvex and NP-hard, so the method cannot obtain its global optimum with known polynomial-complexity algorithms.The paper instead targets a local optimum through iterative convexification.
  • STB-OM optimization: The secrecy rate is monotonically nondecreasing across Algorithm 1 iterations and converges because the transmit-power constraint provides an upper bound.Fig. 4 demonstrates this convergence behavior under different MBS transmit powers.
  • STB-OM formulation: STB-OM requires only local MBS-side CSI, including the channel state information of the macrocell users and eavesdropper.The eavesdropper's CSI is assumed available to make the STB tractable.

B. Secrecy Transmit Beamforming Sequentially Performed in Macrocell and Femtocell (STB-SMF)

STB-SMF exploits cross-tier interference to improve the eavesdropped macrocell user's secrecy rate while protecting legitimate macrocell users. Cooperative femtocells design null-space beamformers, report interference temperatures to the MBS, and enable sequential macrocell beamforming with limited cooperation.

  • Sequential operation: Algorithm 1's performance gap from the globally optimal original problem cannot be provided because obtaining that global optimum is difficult.With proper initial values, the achieved local optimum may equal the global optimum, although finding such initial values is challenging.
  • STB-SMF design: STB-SMF uses null-space beamforming so cooperative FBS interference degrades the eavesdropper while avoiding interference to legitimate macrocell users.The design requires NM > NF > M to guarantee a nonempty null space, then maximizes eavesdropper interference subject to transmit-power constraints.
  • STB-SMF design: The FBS beamforming problem is reformulated as a standard SOCP solvable efficiently by numerical optimization, with a closed-form solution available when each FBS serves one FU.The beamforming vectors are parameterized through a basis for the null space of the collective legitimate-user channels.
  • STB-SMF design: For the single-FU case, the optimal objective equals P_F λmax(R1n, R2n), and the optimal beamforming vector follows the corresponding generalized eigenvector.The generalized eigenvalue and eigenvector determine the optimal solution of the FBS subproblem.
  • Sequential operation: STB-SMF sequentially aggregates each FBS's interference temperature at the eavesdropper, then uses their sum to guide the MBS's STB-OM design.Each FBS sends its scalar interference-temperature metric to the MBS, which computes IFTsum and performs macrocell beamforming.
  • Sequential operation: The scheme reduces cooperation and computation by requiring only scalar feedback from each FBS, but it ignores FU QoS and therefore serves as a preliminary performance-complexity tradeoff.STB-SMF accounts for MU QoS while not ensuring or enhancing FU QoS.

C. Secrecy

The paper develops STB-JMF, which jointly optimizes macrocell and femtocell beamforming using global CSI to improve secrecy while satisfying legitimate-user QoS. Its formulation is solved through semidefinite relaxation and one-dimensional search, with tighter QoS guarantees but higher computational complexity than earlier schemes.

  • STB-SMF: STB-SMF improves MU1 secrecy by exploiting co-channel interference, but its omission of cooperative-FU QoS prevents guarantees for their sum-rate performance.This limitation motivates the broader QoS treatment in STB-JMF.
  • Transmit Beamforming Jointly Performed in Macrocell and Femtocell (STB-JMF): STB-JMF jointly optimizes MBS and cooperative-FBS beamforming from globally shared CSI to improve MU1 secrecy while satisfying MUs’ and FUs’ QoS requirements.Cooperative FBSs send local CSI to the MBS, which designs all transmit beamforming vectors jointly.
  • Transmit Beamforming Jointly Performed in Macrocell and Femtocell (STB-JMF): The STB-JMF optimization is reformulated with semidefinite relaxation, a Charnes–Cooper transformation, and an SDP solved inside a one-dimensional search over the eavesdropper SINR.The original nonconvex problem is divided into an outer line search and an inner SDP.
  • Transmit Beamforming Jointly Performed in Macrocell and Femtocell (STB-JMF): Semidefinite relaxation is always tight for STB-JMF because the relevant solution is guaranteed to be rank one.The proposition establishes a rank-one solution for the specified femtocell matrix, yielding an exact beamforming recovery for that component.
  • Transmit Beamforming Jointly Performed in Macrocell and Femtocell (STB-JMF): Unlike STB-SMF, STB-JMF accounts for QoS requirements of all legitimate macrocell and cooperative-femtocell users while enhancing the eavesdropped MU’s secrecy rate.STB-SMF deliberately exploits co-channel interference but ignores co-channel-FU QoS, whereas STB-JMF includes both user classes.

IV. SIMULATION RESULTS AND DISCUSSIONS

The simulations model a downlink HetNet with a central MBS, Poisson-distributed FBSs, and a 500 m macrocell region. The authors report that two cooperative FBSs are sufficient for good secrecy performance, while additional FBSs may provide little further improvement.

  • IV. SIMULATION RESULTS AND DISCUSSIONS: The simulation uses a central MBS covering a circular 500 m region, with FBSs distributed according to a Poisson point process.Femtocells are generated through Voronoi tessellation within the cellular coverage.
  • IV. SIMULATION RESULTS AND DISCUSSIONS: Two cooperative FBSs are reported as sufficient for good secrecy performance because adding more FBSs increases interference without notable additional secrecy improvement.The reported numerical results are omitted due to page limitations.

A. Benchmark Scheme

The benchmark maximizes MU1’s ordinary rate without secrecy considerations, then evaluates its secrecy rate using those non-secrecy-oriented beamformers. It retains transmit-power and legitimate-user QoS constraints and is transformed into an SDP by dropping a rank-one constraint.

  • A. Benchmark Scheme: The benchmark first maximizes MU1’s rate without secrecy and then measures its secrecy rate using the resulting beamforming vectors.The benchmark therefore represents non-secrecy-oriented beamforming evaluated under the secrecy metric.
  • A. Benchmark Scheme: The benchmark optimization retains transmit-power constraints and QoS requirements for legitimate MUs and FUs.The constraints cover both macrocell users and users in cooperative femtocells.
  • A. Benchmark Scheme: The nonconvex benchmark problem is converted into an SDP by dropping a rank-one constraint.The resulting SDP is convex and follows the same transformation approach described for the secrecy design.
  • A. Benchmark Scheme: Figure 7 compares MU1 secrecy rate against MBS transmit power, with two FBSs generating interference in the STB-SMF and STB-JMF schemes.The figure defines the benchmark comparison’s horizontal variable and cooperative-FBS setting.

B. Performance of the Proposed Schemes

The proposed STB schemes improve secrecy-rate performance while addressing the QoS of legitimate users in the two-tier HetNet. STB-JMF provides stronger femtocell-user SINR protection, whereas STB-SMF can achieve slightly higher secrecy rates when femtocell QoS is not enforced.

  • STB-SMF slightly outperforms STB-JMF across MBS transmit-power values because it does not consider femtocell-user QoS.All proposed schemes improve faster than the benchmark as MBS transmit power increases.
  • STB-SMF and STB-JMF achieve higher secrecy rates than the benchmark, even with relatively low transmit power at each FBS.The benchmark catches up only at very high FBS power, while the proposed schemes provide high secrecy rates with little FBS transmit power.
  • STB-JMF achieves substantially better femtocell-user SINR than STB-SMF as MBS transmit power increases.Under STB-SMF, femtocell-user SINR drops dramatically because additional interference is introduced at femtocell users.
  • STB-JMF maintains femtocell-user QoS through joint design, although its SINR constraint becomes infeasible at low FBS power.With a 0.60 SINR requirement, the constraint cannot be satisfied around 20 dBm, so the requirement is reduced to 0.5 for that case.

C. Impact of Artificial Noise (AN) on the Proposed Schemes

The simulations compare artificial-noise variants with the proposed STB schemes in broadcast and interference channels. The proposed schemes show nearly unchanged secrecy rates when artificial noise is jointly designed or omitted.

  • The simulations evaluate artificial noise in STB-OM, STB-SMF, and STB-JMF alongside additional comparison schemes.The comparison covers broadcast-channel and interference-channel settings.
  • STB-SMF and STB-JMF are evaluated as interference-channel schemes with two four-antenna transmitters, two single-antenna receivers, and one single-antenna eavesdropper.The eavesdropper attempts to wiretap one transmitter.
  • The proposed schemes achieve almost the same secrecy rate with or without jointly designed artificial noise.This holds in both the broadcast-channel and interference-channel simulations.
  • Interference from other legitimate transmissions can serve as effective artificial noise at the eavesdropper.In STB-OM, other macrocell-user data acts as interference; in the cooperative schemes, femtocell data can play the same role.

V. CONCLUSIONS

The paper develops three secrecy transmit beamforming schemes for two-tier HetNets under orthogonal and secrecy-oriented non-orthogonal spectrum allocation. Reformulated SDP and SOCP solutions yield effective secrecy-rate performance, while multiple eavesdroppers, targeted users, and imperfect CSI remain future extensions.

  • Three STB schemes—STB-OM, STB-SMF, and STB-JMF—are proposed under OSA and SONOSA to maximize the secrecy rate of the eavesdropped user.
  • The nonconvex STB optimization problems are reformulated and solved using semidefinite-programming and second-order-cone-programming techniques.
  • Simulation results show the effectiveness of the proposed schemes.
  • Future work includes multiple eavesdroppers or targeted macrocell users and robust STB under imperfect CSI.

APPENDIX

The appendix establishes optimality properties for the reformulated optimization problem using Slater and KKT conditions. It proves that the relevant optimal transmit covariance matrices have rank one.

  • Problem (37) satisfies Slater’s condition, making the KKT conditions sufficient and necessary for optimality.
  • The rank-one result follows from the stated rank bound on G*_1 together with X*_1 ≠ 0, and the same procedure is applied to the remaining matrices.
  • The optimal power constraints are active at equality, implying positive optimal dual-related quantities.
  • The proof shows that the optimal covariance matrices X*_1 and X*_nk have rank one.The argument applies for n ∈ [1,N] and k ∈ [1,K].
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