PaperlayerView exact revision on arXiv

Source-linked AI summary

Achieving Covert Wireless Communications Using a Full-Duplex Receiver

Khurram Shahzad, Xiangyun Zhou, Shihao Yan, Jinsong Hu, Feng Shu, Jun Li

arXiv:1810.06741v1cs.IT

TL;DR

The paper addresses how to hide Alice’s transmission from Willie while preserving communication to Bob over fading channels. It uses a full-duplex receiver with randomized artificial-noise power, derives Willie’s optimal detection performance, and optimizes the noise range and transmission prior. The analysis shows that artificial-noise power requires careful control because of self-interference, and that a transmission prior of 0.5 is not always optimal.

  • Problem

    Covert communications must hide a transmission from Willie while maintaining decoding performance at the intended receiver.

  • Method

    Bob operates full-duplex, transmits artificial noise with randomized power, and the paper analyzes Willie’s radiometer while optimizing artificial-noise power and Alice’s transmission prior.

  • Results

    For τ ≥0.44, the proposed joint optimization scheme provides a significant gain in achievable covertness, while its detection-error performance decreases gradually as the rate requirement increases.

  • Takeaways & Limitations

    Artificial noise can provide covertness despite self-interference, but its transmit-power levels must be managed carefully and a prior transmission probability of 0.5 is not always best.

Abstract

from arXiv · show

Covert communications hide the transmission of a message from a watchful adversary while ensuring a certain decoding performance at the receiver. In this work, a wireless communication system under fading channels is considered where covertness is achieved by using a full-duplex (FD) receiver. More precisely, the receiver of covert information generates artificial noise with a varying power causing uncertainty at the adversary, Willie, regarding the statistics of the received signals. Given that Willie's optimal detector is a threshold test on the received power, we derive a closed-form expression for the optimal detection performance of Willie averaged over the fading channel realizations. Furthermore, we provide guidelines for the optimal choice of artificial noise power range, and the optimal transmission probability of covert information to maximize the detection errors at Willie. Our analysis shows that the transmission of artificial noise, although causes self-interference, provides the opportunity of achieving covertness but its transmit power levels need to be managed carefully. We also demonstrate that the prior transmission probability of 0.5 is not always the best choice for achieving the maximum possible covertness, when the covert transmission probability and artificial noise power can be jointly optimized.

I. INTRODUCTION

The paper studies covert wireless communication using a full-duplex receiver that generates artificial noise, and develops analytical and design tools for confusing Willie over fading channels.

  • Proposed approach: Full-duplex reception enables Bob to generate artificial noise with varying power, deliberately confusing Willie about Alice’s covert transmission.The scheme uses Bob’s artificial noise as a cover while Alice transmits to Bob.
  • Analytical characterization: The paper derives Willie’s optimal radiometer threshold and minimum detection error probability under the considered fading-channel model.These results characterize Willie’s detection performance for the proposed covert communication setting.
  • System design: For a given covert-rate requirement, the authors optimize the artificial-noise power range and Alice’s prior transmission probability to maximize Willie’s expected detection errors.The design jointly considers parameters controlled by the communication pair.
  • System design: An a priori transmission probability of 0.5 is not always optimal; increasing it beyond 0.5 can allow higher artificial-noise power while maintaining the same rate requirement.The authors connect this adjustment to the achievable level of covertness.
  • System trade-off: Artificial noise creates covertness but also causes full-duplex self-interference, so its transmit power must be controlled carefully to preserve covert information transfer.The receiver’s residual self-interference degrades the message’s signal-to-noise ratio.

B. Proposed Transmission Scheme

Bob continuously transmits artificial noise with a slot-varying, unknown instantaneous power distribution, while Willie detects Alice’s activity per slot using received-power observations.

  • Artificial-noise transmission: Bob’s artificial-noise power varies independently across slots according to a continuous uniform distribution over [Pmin, Pmax].Willie knows the distribution but not the exact power used in a particular slot.
  • Artificial-noise transmission: Bob transmits artificial noise continuously, whether or not Alice transmits, while the scheme hides Alice’s existence and message transmission rather than Bob’s presence.Bob therefore acts as both information receiver and cooperative jammer.
  • Detection objective: Willie makes a per-slot decision about Alice’s transmission, because the communication spans many slots and Alice’s transmission probability affects detection performance and covert throughput.Detecting when transmissions occur can also help Willie identify future transmission patterns.
  • Detection objective: Willie uses a radiometer, or threshold test on average received power, because this statistic is sufficient for his hypothesis test.The hypotheses represent Alice not transmitting versus transmitting to Bob.
  • Detection analysis: Willie’s minimum detection error is zero when the condition for overlapping decision regions does not hold; otherwise, an optimal threshold and nonzero error probability exist.The receiver-noise variance is needed to calculate the optimal threshold but does not affect the minimum detection error as n →∞.

IV. PERFORMANCE OF COVERT COMMUNICATION

The section characterizes Bob’s transmission performance under fading and a fixed Alice-to-Bob rate. It identifies transmission outage as the event that channel capacity falls below the required rate and derives its probability.

  • Transmission outage: The analysis retains the square-root law as a reference point when Willie has perfect statistical knowledge of the test statistics.Prior work indicates that uncertainty in Willie’s test statistics can permit a positive covert transmission rate.
  • Transmission outage: The SINR at Bob when Alice transmits is defined using Alice’s received signal, residual self-interference from Bob’s AN, and receiver noise.The corresponding SINR expression is introduced for evaluating Bob’s decoding performance.
  • Transmission outage: A transmission outage occurs when Bob’s channel capacity C_ab is below the predetermined rate R_ab.The outage depends on the random channel gains h_ab and h_bb and Bob’s artificial-noise power P_b.
  • Transmission outage: Lemma 1 gives a closed-form expression for the transmission outage probability from Alice to Bob.The derivation integrates over the distributions of the channel gains and Bob’s AN power.

B. Expected Detection Error Probability at Willie

This section evaluates Willie’s expected detection error probability over fading under the optimal detection threshold. It also identifies how AN power bounds and Alice’s transmit power affect achievable covertness.

  • Expected detection error probability: Lemma 2 gives Willie’s expected detection error probability under the optimal detection threshold.The expectation is taken over channel realizations involving Alice, Bob, and Willie.
  • Expected detection error probability: The parameter t is defined by the ratio of Willie’s channel and Alice’s power term to the combined AN-power-range term.Specifically, t depends on λ_bw, P_a, λ_aw, P_max, and P_min.
  • Expected detection error probability: The derivation treats separately the cases π_1 ≥ π_0 and π_0 > π_1 when evaluating Willie’s detection errors.Both cases are obtained by integrating over the relevant fading distributions and applying total expectation.
  • Power effects: As P_max approaches infinity, Willie’s detection-error probability approaches π_0 or π_1, depending on the respective prior-probability case.This limiting value represents the maximum expected detection error probability P_E* for those priors.
  • Power effects: As Alice’s transmit power P_a approaches infinity, t approaches 1 and the expected detection error probability approaches zero.Thus, for fixed P_min and P_max, sufficiently high Alice transmit power makes the covert transmission detectable by Willie.

V. COVERT COMMUNICATION DESIGN

The design problem maximizes Willie’s detection errors while satisfying Bob’s covert-rate and average-AN-power constraints. The controllable design variables are Bob’s AN-power range and Alice’s transmission priors.

  • Design objective: The design objective is to maximize Willie’s detection-error probability rather than impose a fixed covertness constraint.The optimization also requires an average power constraint and a minimum effective covert-rate requirement τ.
  • Design variables: Alice’s transmission priors π_0 and π_1, with π_0 = 1 − π_1, and Bob’s AN-power bounds P_min and P_max are the principal design parameters.Alice’s transmit power P_a is fixed and is assumed sufficient to meet the rate requirement without AN.
  • Constraints: The optimization includes transmission outage probability δ_ab, minimum covert rate τ, and Bob’s average AN power P_avg.The outage probability depends on the AN-power bounds, and the expected detection error is supplied by Lemma 2.
  • Solution strategy: The problem is solved step by step to obtain a globally optimal solution and insights into how system parameters affect covertness.The formulation explicitly balances the covert-rate requirement against Willie’s expected detection errors.

A. Optimal Minimum AN Power

For fixed maximum AN power and transmission priors, the section determines the minimum AN power that maximizes Willie’s expected detection error while meeting Bob’s covert-rate requirement. The optimum is the smallest feasible lower bound.

  • Optimization setup: For a fixed average AN power, the design minimizes Bob’s transmission outage probability while maximizing Willie’s expected detection error.This couples the covert-rate constraint with the covertness objective.
  • Optimization setup: The optimal P_min is selected for each given P_max and prior-probability pair {π_0, π_1}.Proposition 2 addresses the choice of minimum AN power under the effective covert-rate requirement.
  • Monotonicity analysis: The function κ(t) governing the expected detection error is analyzed through its derivative over t ∈ [0, 1).Its derivative reaches its maximum value −ln 2 at t = 1/2, while t is nondecreasing in P_min.
  • Optimal minimum AN power: P_min = 0 is optimal because the expected detection error decreases as P_min increases.This choice is made while preserving the covert-rate feasibility condition established for the AN-power range.
  • Covert-rate constraint: The covert-rate analysis shows that transmission outage probability increases with P_min, so the rate constraint upper-bounds the allowable minimum AN power.The upper bound is obtained by solving the constraint at equality.

B. Optimal Priors for Alice’s Transmission

The optimal prior probability of Alice’s covert transmission depends on Bob’s maximum artificial-noise power, rather than being fixed universally at 0.5. Jointly selecting these parameters balances Willie’s detection errors against the covert rate requirement and self-interference.

  • Optimal prior selection: Proposition 3 gives Alice’s optimal transmission prior as a function of Bob’s maximum artificial-noise power, Pmax.The optimization considers the cases π1 < π0 and π1 ≥ π0 under the rate-feasibility constraint.
  • Optimization cases: The derivative signs in the two prior-probability cases determine which feasible boundary or interior choice is optimal.For π1 < π0, the derivative is nonnegative; for π1 ≥ π0, the derivative is nonpositive over the stated range.
  • Dependence on AN power: The optimal prior π1 depends on Pmax, so it may equal 0.5 for some choices but not for others.Pmax directly affects the transmission outage probability through receiver self-interference.
  • Joint design objective: The prior and AN-power choices must jointly satisfy the covert rate requirement while maximizing Willie’s expected detection error.The paper frames their interaction as an interplay between rate feasibility and detection-error maximization.

C. Optimal Maximum AN Power

The paper selects Bob’s maximum artificial-noise power by combining rate feasibility, average-power constraints, and Willie’s expected detection error. The resulting design is globally optimized and shows that self-interference must be managed alongside covertness.

  • Optimal maximum AN power: Proposition 4 gives Bob’s optimal maximum AN power under the average power constraint Pavg.The solution is derived after optimizing Pmin and Alice’s prior probability.
  • Optimization procedure: The optimization over Pmax is one-dimensional and can be solved by efficient numerical search after the prior-dependent objective is formed.The objective need not be monotonic because increasing Pmax decreases p(Pmax) while increasing q(Pmax).
  • Global optimization: The globally optimal solution is obtained sequentially by optimizing Pmin, then Alice’s prior π1, and finally Pmax.The paper summarizes the resulting global solution using the expressions for P∗max in (35)–(36).
  • Parameter effects: Higher self-interference coefficient φ requires a lower optimal P∗max and decreases achievable covertness.The paper therefore recommends avoiding drastic changes in P∗max while accounting for the rate requirement and self-interference trade-off.
  • Rate and covertness trade-off: The optimal Pmax can satisfy the covert-rate requirement with bare equality while maximizing Willie’s expected detection error.When π1 = 0.5 is not optimal, adjusting Alice’s prior helps meet the rate requirement while keeping detection error high.

VI. NUMERICAL RESULTS AND DISCUSSION

The numerical results show how Alice’s power, Bob’s self-interference cancellation, covert-rate requirements, and transmission probability shape the optimized covertness performance. Jointly optimizing Alice’s transmission probability and Bob’s artificial-noise power is especially beneficial at higher covert-rate requirements.

  • Higher Alice transmit power permits a higher optimal maximum artificial-noise power while satisfying the covert-rate requirement.
  • Poorer self-interference cancellation requires lower optimal artificial-noise power, which adversely affects achievable covertness.A higher φ represents poorer cancellation; reducing Pmax decreases confusion at Willie.
  • For a fixed Alice transmit power, π1 = 1/2 is optimal up to a covert-rate threshold, after which the optimal π1 increases.Increasing Alice’s transmit power shifts this behavior toward a somewhat higher τ.
  • As covert-rate requirements increase, Bob may reduce Pmax to limit self-interference, but this lowers the optimized detection error probability at Willie.The results link reduced artificial-noise power with less confusion in Willie’s received-signal statistics.
  • For τ ∈[0, 0.44], joint optimization matches the π1 = 0.5 benchmark, whereas for τ ≥0.44 it provides a significant covertness gain.At higher rate requirements, joint optimization decreases gradually while the benchmark drops sharply; the benchmark has a particularly poor result at τ = 0.5.

VII. CONCLUSION

The paper analyzes covert communication using a full-duplex receiver that emits randomized artificial noise to induce detection errors at Willie. It provides design guidance for artificial-noise power and transmission probability, while noting self-interference and an asymptotic-slot limitation.

  • VII. CONCLUSION: A full-duplex receiver generates artificial noise to cause detection errors at Willie over fading wireless channels.Willie uses a radiometer, and the paper characterizes his optimal detection performance conditioned on fading realizations.
  • VII. CONCLUSION: The analysis provides design guidelines for selecting the artificial-noise transmit-power range and covert-transmission probability.These parameters are chosen to maximize the expected detection error probability at Willie while supporting covert communication.
  • VII. CONCLUSION: Artificial noise can provide covertness, but its power must be controlled because full-duplex self-interference affects covert-information transfer.The receiver’s artificial-noise levels therefore involve a covertness–self-interference trade-off.
  • VII. CONCLUSION: A covert-transmission prior of 0.5 is not always optimal for achieving the best possible covertness.The paper reports this result when covert-transmission probability and artificial-noise power are jointly optimized.
  • VII. CONCLUSION: The current work assumes n →∞, while future work will consider finite n for more precise results.The stated future direction concerns communication systems where finite blocklength effects matter.

APPENDIX A PROOF OF PROPOSITION 1

The proof analyzes Willie’s threshold choices by partitioning the threshold into intervals determined by received-power boundaries. It evaluates false alarms, missed detections, and detection error probability across these cases to identify the optimal threshold.

  • APPENDIX A PROOF OF PROPOSITION 1: Willie’s threshold is analyzed over intervals marked by received-power quantities involving Pmin, Pmax, artificial-noise power, and receiver noise.The cases are graphically represented for different orderings of these boundary quantities.
  • APPENDIX A PROOF OF PROPOSITION 1: For γ < |hbw|2Pmin+σ2_w, the false-alarm probability is 1, the missed-detection probability is 0, and PE = π0.This threshold region yields detection error determined by the prior probability π0.
  • APPENDIX A PROOF OF PROPOSITION 1: For γ > |hbw|2Pmax+|haw|2Pa+σ2_w, the false-alarm probability is 0, the missed-detection probability is 1, and PE = π1.This region yields detection error determined by the prior probability π1.
  • APPENDIX A PROOF OF PROPOSITION 1: In one interval, PF A = 0 and PMD = 0, so choosing γ there produces no detection errors at Willie.The proof identifies this interval as a distinct threshold case.
  • APPENDIX A PROOF OF PROPOSITION 1: Willie chooses the optimal threshold using the prior probabilities π0 and π1, after which PE is obtained from the corresponding Case-II expressions.The proof also uses the sign of the partial derivative with respect to γ to determine threshold choices within cases.
Loading 1810.06741v1…