The misuse of wireless communications by malicious users imposes new threats on the public security, and authorized parities need to intervene in the malicious communication links over the air. This paper investigates this emerging wireless communication intervention problem at the physical layer. Unlike prior studies using jamming to disrupt or disable the targeted wireless communications, we propose a new physical-layer spoofing approach to change their communicated information. Consider a fundamental three-node system over additive white Gaussian noise (AWGN) channels, in which an intermediary legitimate spoofer aims to spoof a malicious communication link from Alice to Bob, such that the received message at Bob is changed from Alice's originally sent message to the one desired by the spoofer. We propose a new symbol-level spoofing scheme, where the spoofer designs the spoofing signal via exploiting the symbol-level relationship between each original constellation point of Alice and the desirable one of the spoofer. In particular, the spoofer aims to minimize the average spoofing-symbol-error-rate (SSER), which is defined as the average probability that the symbols decoded by Bob fail to be changed or spoofed, by designing its spoofing signals over symbols subject to the average transmit power constraint. By considering the case when Alice employs the widely- used binary phase-shift keying (BPSK) modulation, we obtain the optimal solution to the average SSER minimization problem. Numerical results show that the symbol-level spoofing scheme with optimized transmission achieves a much lower average SSER, as compared to other benchmark schemes.
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