An MMSE Approach to the Secrecy Capacity of the MIMO Gaussian Wiretap Channel. (27th July 2009)

• Record Type: Journal Article
• Authors: Bustin, Ronit; Liu, Ruoheng; Poor, H. Vincent; Shamai (Shitz), Shlomo
• Other Names: Debbah Mérouane Academic Editor.
• Is Part Of: EURASIP journal on wireless communications and networking. Volume 2009(2009)
• Publication Date: 2009-07-27
• Subjects: Wireless communication systems -- Periodicals; Signal processing -- Periodicals; 621.38405
• DOI: 10.1155/2009/370970
• Languages: English
• ISSNs: 1687-1499

Abstract

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 the missing 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.