An MMSE approach to the secrecy capacity of the MIMO Gaussian wiretap channel

Authors:
Ronit Bustin;Ruoheng Liu;H. Vincent Poor;Shlomo Shamai
Affiliations:
Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, Israel;Department of Electrical Engineering, Princeton University, Princeton, NJ;Department of Electrical Engineering, Princeton University, Princeton, NJ;Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, Israel
Venue:
EURASIP Journal on Wireless Communications and Networking - Special issue on wireless physical layer security
Year:
2009

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Abstract

This paper provides a closed-form expression for the secrecy capacity of the multiple-input multiple output (MIMO) Gaussian wiretap channel, under a power-covariance constraint. Furthermore, the paper specifies the input covariance matrix required in order to attain the capacity. The proof uses the fundamental relationship between information theory and estimation theory in the Gaussian channel, relating the derivative of the mutual information to the minimum mean-square error (MMSE). The proof provides themissing intuition regarding the existence and construction of an enhanced degraded channel that does not increase the secrecy capacity. The concept of enhancement has been used in a previous proof of the problem. Furthermore, the proof presents methods that can be used in proving other MIMO problems, using this fundamental relationship.