Secure Communications in Millimeter Wave Ad Hoc Networks

I. INTRODUCTION

• Higher-layer key distribution and management can burden confidential communication in decentralized ad hoc networks, motivating physical-layer security.The paper explores physical-layer security by leveraging wireless-channel randomness.Source: §I · p. 1

A. Related Works and Motivation

• Prior physical-layer secrecy studies in ad hoc networks primarily addressed lower-frequency links, while mmWave ad hoc secrecy remained comparatively less developed.The paper also describes mmWave links as more random and harder to intercept than lower-frequency counterparts.Source: A. Related Works and Motivation · pp. 1–2

B. Approach and Contributions

• The paper characterizes mmWave channel and blockage effects, develops a tractable ULA secrecy-rate evaluation, and examines antenna gains, node density, frequency, and artificial noise.Its reported findings include a transmit-power-dependent frequency transition and the effect of transmitter antenna count on eavesdropper gain.Source: B. Approach and Contributions · p. 2

II. SYSTEM DESCRIPTION

• The network model uses randomly located transmitting nodes and eavesdroppers, directional sectored antennas, and LoS/NLoS links under blockage.The transmitter-receiver distance is fixed in the stated model.Source: §II · pp. 2–3

III. SECRECY EVALUATION

• Average achievable secrecy rate is evaluated from the legitimate-link rate and the most malicious eavesdropper's rate.The secrecy-rate expression uses the positive difference between the two rates; the paper derives an exact average rate for each link.Source: §III · pp. 3–4
• The legitimate-link average rate is achievable because rapid mmWave channel fluctuations allow coding across many coherence intervals.The transmitter's rate depends on its channel to the intended receiver because passive eavesdroppers' channel state information is unavailable to it.Source: §III · p. 3
• The legitimate-link average rate decreases with transmitting-node density and increases with narrower beams, which also allow more transmitters in the network.The stated density effect is attributed to greater interference from additional transmitting nodes.Source: §III · p. 4
• The exact average rate of the most malicious eavesdropper is derived, and combining link-rate expressions evaluates the network's average achievable secrecy rate.The eavesdropper rate is specified in Theorem 3.Source: §III · p. 4

A. Simplified LoS MmWave Model

• The simplified model treats a link as LoS when its distance is below DLoS and as outage otherwise.For an established LoS link, the intended-receiver average rate from Theorem 1 can be simplified.Source: A. Simplified LoS MmWave Model · p. 4
• The intended-receiver average rate decreases with transmitting-node density, while the most-malicious-eavesdropper average rate increases with eavesdropper density.The former follows from added interference; the latter reflects the increasing number of eavesdroppers.Source: A. Simplified LoS MmWave Model · p. 5
• Substituting the intended-receiver and most-malicious-eavesdropper rate expressions into (6) yields the average achievable secrecy rate.Source: A. Simplified LoS MmWave Model · p. 5

B. Uniform Linear Array

• The ULA model places array elements along the propagation-plane y-axis and uses azimuth departure and arrival angles uniformly distributed on [0, 2π].Each receiver has the same number of antennas as its transmitting node, and all nodes use matched-filter beamforming.Source: B. Uniform Linear Array · p. 5
• The analysis lower-bounds the intended-receiver average rate and gives a lower bound on achievable secrecy rate for the ULA configuration.Source: B. Uniform Linear Array · pp. 5–6
• Adding antennas at the transmitting node decreases the antenna gain obtained by eavesdroppers, weakening their received signal.Source: B. Uniform Linear Array · p. 6

IV. ARTIFICIAL NOISE AIDED TRANSMISSION

• The total transmit power is split as PS = μPt for information and PA = (1 − μ)Pt for artificial noise.Here μ is the fraction of power assigned to the information signal.Source: §IV · p. 6
• Because the transmitter's artificial-noise beam is not directed toward the intended receiver, its effect there is negligible.The section separately specifies SINR expressions for the intended receiver and the most malicious eavesdropper.Source: §IV · p. 6
• The section derives exact average-rate expressions for the intended receiver and the most malicious eavesdropper, plus a lower bound for the intended-receiver rate.Source: §IV · pp. 6–7
• Combining the intended-receiver and eavesdropper rates yields the average achievable secrecy rate for artificial-noise-aided transmission.Source: §IV · pp. 6–7

V. NUMERICAL RESULTS

• The evaluation assumes an exponential LoS probability function with 1/̺ = 141.4 m.Source: §V · p. 7
• The numerical setup uses a 2 GHz mmWave bandwidth, a 10 dB noise figure, and reference distance d = 1.Source: §V · p. 7
• The evaluated carrier frequencies are 28, 38, 60, and 73 GHz, with LoS and NLoS path-loss exponents based on practical channel measurements.Source: §V · p. 7

• At low transmit power, 28 GHz gives better secrecy; as power rises, 60 and 73 GHz achieve higher rates, with an optimum power at each tested frequency.At sufficiently high power, 60 GHz also outperforms 73 GHz.Source: Figure 1 · p. 8, A. Average Achievable Secrecy Rate · p. 8
• Increasing transmitting-node density lowers average secrecy rate at 60 GHz as interference becomes dominant in dense networks.The analysis also reports that more eavesdroppers harm secrecy.Source: Figure 2 · p. 8, A. Average Achievable Secrecy Rate · p. 8
• With UPA, secrecy is lower for Ne = 16 than Ne = 4 because eavesdroppers obtain more effective antenna gain.Source: A. Average Achievable Secrecy Rate · p. 8
• As communication distance grows, secrecy rate significantly decreases because the intended-link rate falls while the most malicious eavesdropper’s rate remains unchanged.Source: A. Average Achievable Secrecy Rate · p. 9

• More transmitting antennas increase average secrecy, while more eavesdropper antennas decrease it; secrecy becomes very small with only a couple of transmitting antennas.The paper attributes this to a wider information beam that lets more eavesdroppers receive strong signals.Source: Figure 4 · p. 9, B. average achievable secrecy rate… · p. 9
• Increasing eavesdropper or transmitting-node density reduces secrecy; transmitter interference remains a concern in very dense networks without highly directional antennas.Source: Figure 5 · p. 9, B. average achievable secrecy rate… · p. 9

C. average achievable secrecy rate with Artificial Noise

• At low node density, AN with µ = 0.85 may not improve secrecy; more power should instead go to the information signal.The passage attributes this to the need to combat interference and mmWave pathloss.Source: C. average achievable secrecy rate… · p. 10
• At 28 GHz, secrecy is higher than at 38 GHz, and AN cannot improve it in the described transmit-power regime.The reported lower bounds approximate the exact results when transmit power is below 30 dBm in this figure.Source: C. average achievable secrecy rate… · p. 10
• An optimal power-allocation factor µ exists for maximizing secrecy; larger communication distance worsens performance, while 28 GHz remains better than 38 GHz at a given distance.The AN benefit depends on setting the allocation between the information signal and AN appropriately.Source: C. average achievable secrecy rate… · p. 10

VI. CONCLUSION

• The paper develops a tractable average-secrecy-rate evaluation for ULA and concludes that power allocation between information and AN must be chosen carefully.The evaluation derives rates with and without AN.Source: §VI · pp. 10–11
• In dense networks, nearby-node interference dominates secrecy performance; the analysis assumes a constant transmitter–receiver distance r.The paper identifies dynamic r and antenna-pattern models for large antenna counts as future work.Source: §VI · p. 11

APPENDIX A: A DETAILED DERIVATION OF THEOREM 1

• The derivation treats desired-signal power and interference as independent, with the desired signal depending on whether the link is LoS or NLoS.It then uses total expectation for one term and a Laplace transform of interference for another.Source: Appendix A · p. 11
• Thinning divides transmitting nodes into independent LoS and NLoS Poisson point processes, whose densities are weighted by the LoS probability.The Laplace functional is applied to obtain the interference term.Source: Appendix A · p. 11

APPENDIX B: A DETAILED DERIVATION OF EQ. (10)

• The receiver-rate derivation uses a lower bound and conditions on whether the typical link is LoS or NLoS.The LoS and NLoS path-loss exponents are denoted αLoS and αNLoS.Source: Appendix B · p. 11
• Jensen’s inequality and the average array gain are used to bound and evaluate terms in the receiver-rate expression.Campbell’s theorem is used in the average-array-gain calculation.Source: Appendix B · p. 11

APPENDIX C: A DETAILED DERIVATION OF THEOREM 2

• Thinning separates eavesdroppers into LoS and NLoS Poisson point processes, with densities weighted by the corresponding LoS probabilities.These processes are used to form the eavesdropper-SINR CDF.Source: Appendix C · p. 12
• The expression being developed uses the CDF of the strongest eavesdropper SINR, Fγe∗(·).The derivation defines the CDF before splitting eavesdroppers by LoS status.Source: Appendix C · p. 12
• The derivation obtains P1(x) first, using the Laplace functional and total probability to calculate Θ.P1(x) is substituted into the preceding expression before deriving P2(x).Source: Appendix C · p. 12