Beamforming is a powerful tool for physical layer security, as it can be used for steering signals towards legitimate receivers and away from eavesdroppers. An active eavesdropper, however, can interfere with the pilot phase that the transmitter needs to acquire the channel knowledge necessary for beamforming. By doing so, the eavesdropper can make the transmitter form beams towards the eavesdropper rather than towards the legitimate receiver. To mitigate active eavesdroppers, we propose VILLAIN, a novel channel estimator that uses secret pilots. When an eavesdropper interferes with the pilot phase, VILLAIN produces a channel estimate that is orthogonal to the eavesdropper's channel (in the noiseless case). We prove that beamforming based on this channel estimate delivers the highest possible signal power to the legitimate receiver without delivering any signal power to the eavesdropper. Simulations show that VILLAIN mitigates active eavesdroppers also in the noisy case.

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