[Paper Review] Secure Massive MIMO Transmission in the Presence of an Active Eavesdropper

Yongpeng Wu, Robert Schober+3 more|arXiv (Cornell University)|May 6, 2015

Wireless Communication Security Techniques13 references4 citations

TL;DR

This paper proposes a secure massive MIMO transmission scheme against an active eavesdropper that conducts pilot contamination during uplink training. By leveraging asymptotic analysis and artificial noise (AN) precoding, the authors derive a closed-form optimal power allocation for secrecy rate maximization and propose a null-space precoder exploiting low-rank correlation structure to neutralize eavesdropping, achieving perfect secrecy when user and eavesdropper correlation subspaces are orthogonal.

ABSTRACT

In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output (MIMO) systems in the presence of an active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform towards the eavesdropper, thus increasing its received signal power. We derive an asymptotic achievable secrecy rate for matched filter precoding and artificial noise (AN) generation at the transmitter when the number of transmit antennas goes to infinity. For the achievability scheme at hand, we obtain the optimal power allocation policy for the transmit signal and the AN in closed form. For the case of correlated fading channels, we show that the impact of the active eavesdropper can be completely removed if the transmit correlation matrices of the users and the eavesdropper are orthogonal. Inspired by this result, we propose a precoder null space design exploiting the low rank property of the transmit correlation matrices of massive MIMO channels, which can significantly degrade the eavesdropping capabilities of the active eavesdropper.

Motivation & Objective

• To address the threat of pilot contamination from an active eavesdropper in TDD massive MIMO systems, which degrades legitimate user performance and increases eavesdropping capability.
• To derive an asymptotic achievable secrecy rate expression for matched filter precoding and artificial noise (AN) generation as the number of transmit antennas tends to infinity.
• To determine the optimal power allocation between information signal and artificial noise in closed form to maximize secrecy rate.
• To design a precoding scheme that exploits the low-rank structure of channel correlation matrices to nullify the eavesdropper's channel, especially in correlated fading environments.
• To establish conditions under which the eavesdropper's impact can be completely eliminated, specifically when the signal subspaces of users and the eavesdropper are orthogonal.

Proposed method

• Derives an asymptotic expression for the achievable secrecy rate in massive MIMO systems with matched filter precoding and artificial noise, under large-antenna regime.
• Uses random matrix theory to analyze the asymptotic behavior of signal-to-interference-plus-noise ratio (SINR) at the legitimate user and eavesdropper as the number of antennas approaches infinity.
• Derives a closed-form optimal power allocation policy between the information-bearing signal and artificial noise, based on the asymptotic secrecy rate expression.
• Proposes a null-space precoder that aligns the artificial noise to the null space of the eavesdropper’s correlation matrix, leveraging the low-rank property of massive MIMO channel correlations.
• Analyzes the condition under which the eavesdropper’s channel is completely nullified: when the signal subspace of the legitimate users and the eavesdropper are mutually orthogonal.
• Validates the theoretical results through asymptotic analysis and simulation-based verification of the derived expressions.

Experimental results

Research questions

• RQ1 What is the asymptotic achievable secrecy rate in massive MIMO systems when an active eavesdropper contaminates the uplink pilot training phase?
• RQ2 How should power be optimally allocated between the information signal and artificial noise to maximize secrecy rate in the large-antenna regime?
• RQ3 Under what conditions can the impact of an active eavesdropper be completely eliminated in correlated fading channels?
• RQ4 Can the low-rank structure of massive MIMO channel correlation matrices be exploited to design a precoder that nulls the eavesdropper’s channel?
• RQ5 What is the performance gain of the proposed null-space precoder compared to conventional schemes in the presence of pilot contamination?

Key findings

• The asymptotic achievable secrecy rate is derived in closed form for matched filter precoding and artificial noise generation, enabling precise optimization of system parameters.
• The optimal power allocation between information signal and artificial noise is derived in closed form, showing that the information signal power must be below a threshold for reliable secure transmission in i.i.d. fading channels.
• In correlated fading channels, the eavesdropper’s impact vanishes completely when the signal subspaces of the legitimate users and the eavesdropper are orthogonal.
• The proposed null-space precoder, based on the low-rank property of channel correlation matrices, effectively degrades the eavesdropper’s channel, significantly improving secrecy performance.
• Theoretical analysis confirms that the secrecy rate is maximized when artificial noise is aligned to the null space of the eavesdropper’s correlation matrix, especially when the eavesdropper’s channel is correlated and low-rank.
• Simulation results validate the asymptotic analysis, showing that the derived power allocation and precoding scheme achieve high secrecy rates even under strong pilot contamination.