[Paper Review] Secrecy Rates in the Broadcast Channel with Confidential Messages and External Eavesdroppers

Giovanni Geraci, Sarabjot Singh+3 more|arXiv (Cornell University)|Jun 10, 2013

Wireless Communication Security Techniques27 references4 citations

TL;DR

This paper introduces the broadcast channel with confidential messages and external eavesdroppers (BCCE) to model secure MIMO communications where both malicious users and randomly located external eavesdroppers threaten secrecy. Using large-system analysis combining stochastic geometry and random matrix theory, it derives that the secrecy outage probability and rate loss due to eavesdroppers scale as $\lambda_e / \sqrt{N}$, and proposes a practical regularization parameter rule that achieves near-optimal performance without requiring channel state or eavesdropper location knowledge.

ABSTRACT

In this paper, we consider the broadcast channel with confidential messages and external eavesdroppers (BCCE), where a multi-antenna base station simultaneously communicates to multiple potentially malicious users, in the presence of randomly located external eavesdroppers. Using the proposed model, we study the secrecy rates achievable by regularized channel inversion (RCI) precoding by performing a large-system analysis that combines tools from stochastic geometry and random matrix theory. We obtain explicit expressions for the probability of secrecy outage and an upper bound on the rate loss due to the presence of external eavesdroppers. We show that both these quantities scale as $\frac{λ_e}{\sqrt{N}}$, where $N$ is the number of transmit antennas and $λ_e$ is the density of external eavesdroppers, irrespective of their collusion strategy. Furthermore, we derive a practical rule for the choice of the regularization parameter, which is agnostic of channel state information and location of eavesdroppers, and yet provides close to optimal performance.

Motivation & Objective

• To model a realistic physical layer security scenario where both malicious users and randomly located external eavesdroppers can intercept confidential messages.
• To analyze the secrecy performance of regularized channel inversion (RCI) precoding in the presence of both types of eavesdroppers.
• To quantify the impact of external eavesdroppers on secrecy outage probability and rate loss in large-scale MIMO systems.
• To derive a practical, channel-agnostic rule for setting the RCI regularization parameter that maximizes secrecy rate performance.

Proposed method

• Formulates the BCCE model with a multi-antenna base station, legitimate users, malicious users, and spatially random external eavesdroppers modeled as a Poisson point process.
• Applies large-system analysis using tools from random matrix theory (RMT) to characterize the signal-to-interference-plus-noise ratio (SINR) at legitimate and eavesdropping users.
• Employs stochastic geometry (SG) to model the spatial distribution of external eavesdroppers and derive the distribution of their SINR.
• Derives explicit expressions for the secrecy outage probability and mean secrecy rate under both non-colluding and colluding eavesdropper strategies.
• Uses asymptotic approximations based on RMT to simplify the analysis of SINR distributions and secrecy rates in the large-system limit.
• Proposes a practical regularization parameter rule for RCI that depends only on system parameters and achieves near-optimal secrecy rate without requiring knowledge of eavesdropper locations or channel fluctuations.

Experimental results

Research questions

• RQ1 How does the presence of randomly located external eavesdroppers affect the secrecy outage probability in a MIMO broadcast channel with confidential messages?
• RQ2 What is the scaling behavior of the secrecy outage probability and rate loss with respect to the number of transmit antennas and eavesdropper density?
• RQ3 How does the collusion strategy of external eavesdroppers impact the secrecy performance of RCI precoding?
• RQ4 Can a practical, channel-agnostic regularization parameter be derived for RCI that achieves near-optimal secrecy rate performance?
• RQ5 What is the upper bound on the rate loss due to external eavesdroppers compared to a system with only malicious users?

Key findings

• The large-system secrecy outage probability scales as $\lambda_e / \sqrt{N}$, regardless of whether external eavesdroppers collude or not.
• The upper bound on rate loss due to external eavesdroppers also scales as $\lambda_e / \sqrt{N}$, quantifying the performance penalty from external eavesdropping.
• The proposed regularization parameter rule achieves close-to-optimal secrecy rate performance without requiring knowledge of channel state information or eavesdropper locations.
• The mean secrecy rate in the BCCE is derived explicitly, and its degradation compared to the BCC (without external eavesdroppers) is bounded by the $\lambda_e / \sqrt{N}$ scaling.
• The analysis shows that the secrecy outage probability depends on the SINR distribution at eavesdroppers, which is derived using stochastic geometry for both colluding and non-colluding cases.
• The derived expressions for secrecy outage and rate loss are explicit and depend on system parameters such as transmit power, noise, and eavesdropper density.