The Secrecy Capacity of the MIMO Wiretap Channel

We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers.

💡 Research Summary

The paper addresses the fundamental problem of secure communication over a multiple‑input multiple‑output (MIMO) wiretap channel, where a transmitter equipped with Nₜ antennas sends confidential data to a legitimate receiver with N_b antennas while an eavesdropper equipped with N_e antennas attempts to intercept the transmission. Assuming full channel state information (CSI) at the transmitter for both the legitimate and eavesdropping links, the authors derive the exact secrecy capacity – the maximum rate at which information can be transmitted reliably to the legitimate user while guaranteeing that the eavesdropper obtains zero information.

The main result is an explicit expression for the secrecy capacity:

C_s = max_{Q≽0, tr(Q)≤P}