Secure Transmission with Multiple Antennas II: The MIMOME Wiretap Channel

TL;DR

This paper analyzes the secrecy capacity of a MIMOME Gaussian wiretap channel with multiple antennas, providing a computable characterization, optimal transmission strategies, and conditions for zero capacity, revealing fundamental antenna ratio limits for secure communication.

Contribution

It introduces a saddle point characterization of secrecy capacity, optimal diagonalization-based coding strategies, and antenna scaling laws for secure MIMO communication.

Findings

Secrecy capacity is achieved by diagonalizing channel matrices via generalized SVD.

A semi-blind 'masked' MIMO strategy can be far from capacity at high SNR.

To prevent secure communication, the eavesdropper needs three times as many antennas as sender and receiver combined.

Abstract

The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs 3 times as many antennas as the sender and intended receiver have jointly, and that the optimimum division of antennas between sender and intended receiver is in the ratio of 2:1.