  In this paper, we study the design of secure communication for time division
duplex multi-cell multi-user massive multiple-input multiple-output (MIMO)
systems with active eavesdropping. We assume that the eavesdropper actively
attacks the uplink pilot transmission and the uplink data transmission before
eavesdropping the downlink data transmission of the users. We exploit both the
received pilots and the received data signals for uplink channel estimation. We
show analytically that when the number of transmit antennas and the length of
the data vector both tend to infinity, the signals of the desired user and the
eavesdropper lie in different eigenspaces of the received signal matrix at the
base station provided that their signal powers are different. This finding
reveals that decreasing (instead of increasing) the desired user's signal power
might be an effective approach to combat a strong active attack from an
eavesdropper. Inspired by this observation, we propose a data-aided secure
downlink transmission scheme and derive an asymptotic achievable secrecy
sum-rate expression for the proposed design. For the special case of a
single-cell single-user system with independent and identically distributed
fading, the obtained expression reveals that the secrecy rate scales
logarithmically with the number of transmit antennas. This is the same scaling
law as for the achievable rate of a single-user massive MIMO system in the
absence of eavesdroppers. Numerical results indicate that the proposed scheme
achieves significant secrecy rate gains compared to alternative approaches
based on matched filter precoding with artificial noise generation and null
space transmission.
