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Physical Layer Security in Heterogeneous Cellular Networks
Hui-Ming Wang, Tong-Xing Zheng, Jinhong Yuan, Don Towsley, Moon Ho Lee
TL;DR
Physical layer security in heterogeneous cellular networks lacks a fundamental framework covering randomly located base stations, users, and eavesdroppers. The paper proposes threshold-based truncated-ARSP association and derives tractable connection, secrecy, and throughput analyses, finding that a properly chosen threshold improves secrecy throughput.
Problem
Prior HCN secrecy work lacked a framework accounting for multi-Eve wiretapping, random node locations, and large-scale path loss.
Method
The paper models a K-tier HCN with independent PPP locations and analyzes artificial-noise-aided multi-antenna transmission under truncated-ARSP association.
Results
A properly chosen threshold significantly increases secrecy throughput compared with non-threshold mobile access.
Takeaways & Limitations
Access thresholds should be jointly designed with connection and secrecy constraints rather than set as large as possible.
Abstract
from arXiv · showhide
The heterogeneous cellular network (HCN) is a promising approach to the deployment of 5G cellular networks. This paper comprehensively studies physical layer security in a multi-tier HCN where base stations (BSs), authorized users and eavesdroppers are all randomly located. We first propose an access threshold based secrecy mobile association policy that associates each user with the BS providing the maximum \emph{truncated average received signal power} beyond a threshold. Under the proposed policy, we investigate the connection probability and secrecy probability of a randomly located user, and provide tractable expressions for the two metrics. Asymptotic analysis reveals that setting a larger access threshold increases the connection probability while decreases the secrecy probability. We further evaluate the network-wide secrecy throughput and the minimum secrecy throughput per user with both connection and secrecy probability constraints. We show that introducing a properly chosen access threshold significantly enhances the secrecy throughput performance of a HCN.
I. INTRODUCTION
The paper addresses the missing network-level analysis of physical layer security in heterogeneous cellular networks. It proposes threshold-based association and analyzes reliability, secrecy, and secrecy throughput under realistic multi-tier conditions.
- Motivation: HCNs expose authorized transmissions to eavesdroppers, while prior HCN research largely emphasized throughput and energy efficiency rather than security.The open architecture and wireless broadcast nature make secure transmission a significant design concern.
- Related Work: Prior work lacked a general HCN secrecy framework incorporating multiple eavesdroppers, random node locations, and large-scale path loss.The paper contrasts its scope with work focused on secrecy beamforming under perfectly known eavesdropper CSI.
- Performance Analysis: Larger access thresholds improve connection probability but trade off against secrecy probability, requiring joint design of link quality and secrecy.The paper derives tractable connection and secrecy analyses, including bounds close to exact secrecy values in the high-secrecy regime.
- Design Implications: A properly chosen threshold significantly increases secrecy throughput over non-threshold access, whereas maximizing the threshold is not always best.Idle BSs reduce intra- and cross-tier interference, while thresholding can reserve more power for artificial noise.
- Approach: The proposed policy associates a UE with the BS offering the highest truncated ARSP and leaves it inactive when that value is below an access threshold.This policy also accounts for tier association and BS activation probabilities.
III. USER CONNECTION PROBABILITY
This section defines connection probability for a randomly located UE and characterizes the received signal and interference when it is served by a tier-k BS.
- Definition: Connection probability is the probability that a secret message is decoded by a randomly located UE.The UE is considered in the connection-probability analysis without restricting the statement to a particular tier.
- Signal Model: A typical UE receives its desired information signal from the serving BS plus interference from other same-tier BSs and all other tiers.Interference includes undesired information signals and artificial noise.
- Signal Model: R_k denotes the distance between the typical UE and its serving tier-k BS.
A. General Result
The paper derives accurate and tractable connection-probability expressions for users associated with a tier in a multi-tier HCN, including a simpler interference-limited form. The threshold-dependent expression supports analysis of how access thresholds and network parameters affect connection probability.
- The connection probability is the probability that a tier-k user's instantaneous SINR exceeds the target SINR βt.
- Theorem 1 gives an accurate integral expression for the connection probability of a typical UE associated with tier k.The derivation handles interference through derivatives of its Laplace transform and accounts for exclusion regions around the user.
- The general connection-probability formula is computable without time-consuming Monte Carlo simulations and provides a baseline for approximate results.Its complexity motivates deriving more compact forms for extracting principal properties.
- Figure 4 compares general and interference-limited connection probabilities in a 2-tier HCN under different system parameters.The plotted settings include varying M1 values and fixed powers, densities, target SINR, access probabilities, path-loss exponent, and λ1.
- In the interference-limited HCN, Corollary 1 provides a simpler analytically tractable expression for the connection probability.This case sets thermal noise to zero because aggregate interference is treated as dominant.
- The threshold-dependent term in the connection-probability expression vanishes as τ → 0, recovering non-threshold mobile association.The paper relates this behavior to Dk → ∞ as τ approaches zero.
C. Asymptotic Analysis on Pint
The asymptotic analysis characterizes how access thresholds, densities, transmit powers, and power allocation affect connection and secrecy probabilities in a multi-tier HCN. These parameters create tradeoffs between legitimate-link quality and secrecy.
- Connection probability: As τ → 0, connection probability becomes independent of transmit power and BS density when all tiers share antenna numbers and power allocation ratios.This result assumes Mj = M, φj = φ, and λu ≫ λj for every tier.
- Connection probability: As τ → ∞, connection probability converges to one, while increasing τ improves connection probability but should be properly chosen for secrecy throughput.The access threshold leaves more BSs idle, reducing interference, but excessively large values are not recommended under throughput constraints.
- Connection probability: Increasing the density of other tiers improves connection probability when tier 1 dominates transmit power, whereas increasing user density decreases it through greater interference.A larger access threshold can mitigate this degradation by keeping more BSs idle.
- Connection probability: Connection probability versus P1 is nonmonotonic: it initially increases, then decreases, and eventually levels off as interference offsets signal-power growth.For other tiers, connection probability decreases with P1 and converges to a constant as P1 → ∞.
- Secrecy probability: Secrecy probability decreases with eavesdropper density, access threshold, and power allocation ratios, but increases with user density and serving-tier antenna number.More pico/femto BSs can therefore improve connection probability while reducing secrecy probability, requiring density choices that balance both metrics.
- Secrecy probability: Network interference simultaneously degrades legitimate and wiretap channels, promoting secrecy transmission while restraining legitimate communication.The secrecy analysis considers a worst-case multiuser-decoding Eve that removes interference from information signals and receives artificial noise.
V. NETWORK-WIDE SECRECY THROUGHPUT
The paper defines network-wide secrecy throughput under connection and secrecy probability constraints, then studies how access thresholds, artificial-noise allocation, antennas, and eavesdropper density affect it. A properly chosen threshold balances spatial reuse, secrecy enhancement, and interference to maximize throughput.
- Network-wide secrecy throughput is the achievable secret-message rate per unit area subject to connection and secrecy probability constraints.
- A negative R∗e,k means the connection and secrecy probability constraints cannot be satisfied simultaneously, so transmissions should be suspended.
- More transmit antennas always increase network-wide secrecy throughput, while the optimal information-signal power fraction decreases as eavesdropper density increases.
- A small access threshold improves spatial reuse and secrecy through more active base stations, but added interference reduces legitimate connection probability.
- Network-wide secrecy throughput first increases and then decreases with the access threshold, so an intermediate threshold maximizes performance.
- Under the stated asymptotic conditions, throughput converges to a constant as τ → 0 and tends to zero as τ → ∞; the threshold policy significantly outperforms a non-threshold policy.
A. Average User Secrecy Throughput
This section defines average and minimum per-user secrecy throughput under equal-time-slot TDMA and examines how user, eavesdropper, and antenna densities affect these metrics. More users sharing resources reduce per-user throughput, while additional transmit antennas ameliorate some degradation.
- Average user secrecy throughput is evaluated assuming each base station allocates equal TDMA time slots to associated users in round-robin order.
- The average user secrecy throughput equals the network-wide secrecy throughput after substituting the cell-load expression.
- Minimum average secrecy throughput is defined as the minimum average secrecy throughput achievable across all tiers.
- Average user secrecy throughput deteriorates as eavesdropper density increases, and adding more transmit antennas ameliorates this degradation.
- As user density increases, more UEs share limited resources, decreasing per-user secrecy throughput.
VI. CONCLUSIONS
The paper models a multi-tier HCN with randomly located base stations, users, and eavesdroppers, and develops tractable analyses for secure transmission. It evaluates constrained network-wide and per-user secrecy throughput, with numerical results supporting the analysis.
- The study models base stations, authorized users, and eavesdroppers as independent homogeneous Poisson point processes.
- The proposed truncated-ARSP association policy yields tier-association and base-station-activation probabilities.
- The paper analyzes connection and secrecy probabilities for artificial-noise-aided secure transmission, providing accurate or tractable expressions and approximate secrecy bounds.
- Under connection and secrecy probability constraints, the paper evaluates network-wide secrecy throughput and minimum secrecy throughput per user, supported by numerical results.
APPENDIX
The appendix derives tier-association, base-station-activation, and connection-probability expressions using Poisson point-process analysis. It develops recursive and integral forms for interference and distance distributions used in the main results.
- Tier association requires the typical user’s truncated received power to exceed every competing tier’s truncated received power.
- The tier association probability is obtained by characterizing the absence of competing base stations within tier-dependent regions and applying Poisson point-process properties.
- Base-station activation probability is derived by integrating the probability that users are not associated with a tagged base station, using the PPP probability generating functional.
- The connection probability is expressed through the SINR distribution, interference Laplace transforms, and the probability density of the serving distance.
- A linear recurrence and matrix expressions provide the auxiliary quantities used to calculate the connection probability for multi-antenna transmission.
- The serving-distance density is established separately for distances below and above the tier access threshold, then averaged to complete the connection-probability derivation.
E. Proof of Corollary 1
The proof simplifies the interference-limited expression, rewrites it using the L1 induced matrix norm, and completes the result by averaging over Rk.
- For N0 = 0, the expression in (57) is simplified for the interference-limited case.
- The simplified result is alternatively expressed using the L1 induced matrix norm.
- Averaging over Rk using (58) completes the proof.
F. Proof of Properties 2-5
The proofs establish asymptotic and monotonicity properties of the HCN connection-related expressions across access threshold, power, density, and related parameters.
- Property 3: For the interference-limited HCN, Lemma 4 gives the UCP of a typical UE associated with tier k.
- Property 3: The value of ˆΥk,mβ equals the value of Υk at βt = mβ.
- Property 2: As τ →∞, Ak →0 for k ∈K, yielding the corresponding limiting form of Υk.
- Property 4: SjA1 monotonically increases with τ and λl for l ≠ 1, while decreasing with λu.
- Property 5: As P1 →∞, Pint c,k becomes independent of P1 for every tier k.
G. Proof of Theorem 2
The proof derives an eavesdropper-related probability expression by modeling interference and bounding secrecy performance through the nearest eavesdropper to the serving base station.
- Applying the PGFL over the PPP together with Jensen’s inequality yields an intermediate expression.
- The proof uses independence between U and Ie, and between U and V, with V distributed as Γ(Mk −1, 1).
- The Laplace transform of Ie is derived before obtaining LIje(κ) from the cited expression.
- An upper bound PU s,k is obtained by considering only the nearest Eve to the serving BS.
- Using the nearest-Eve distance density and the complementary SINR probability, integration produces the result in (24).
H. Proof of Properties 6-8
The proofs characterize how secrecy-related quantities vary with eavesdropper density, access threshold, user and tier parameters, and transmit power.
- Property 6: ξk and ψk are independent of λe, while ψk decreases with τ and φl for l ≠ k.
- Property 6: Both ξk and ψk decrease with φk, while ψk increases with λu and ξk remains independent of λu.
- Property 7: λkAkCα,Mk decreases with Mk and increases with λk.
- Property 8: For extremely large Pk, each Pint,o s,k tends to a constant, while limPk→∞χj = 0.
- Proposition 1: With α = 4 and Mk = 2, Proposition 1 substitutes these values into (33) to obtain the stated expression.