Secure Communication in the Low-SNR Regime

• Published in: IEEE transactions on communications Vol. 60; no. 4; pp. 1114 - 1123
• Main Author: Gursoy, M. C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2012; Institute of Electrical and Electronics Engineers
• Subjects: Antennas; Applied sciences; Channel models; Covariance matrix; Energy efficiency; energy per secret bit; Exact sciences and technology; Fading; fading channels; Gaussian channels; Information theory; Information, signal and communications theory; information-theoretic security; low-SNR regime; MIMO systems; Optimization; Radiocommunications; Receivers; secrecy capacity; Secret; Signal to noise ratio; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Fading channels; Fading; MIMO system; energy per secret bit; Gaussian channel; Eigenvalue; low-SNR regime; Eavesdropping; MIMO systems; Wide band; Information protection; Energetic efficiency; secrecy capacity; information-theoretic security; Minimum energy; Energy efficiency; Multiple channel; Secrecy; Antenna array; Telecommunication security; Gaussian channels; Signal to noise ratio; Information theory
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2012.021712.090634

Secrecy capacity of a multiple-antenna wiretap channel is studied in the low signal-to-noise ratio (SNR) regime. Expressions for the first and second derivatives of the secrecy capacity with respect to SNR at SNR = 0 are derived. Transmission strategies required to achieve these derivatives are identified. In particular, it is shown that it is optimal in the low-SNR regime to transmit in the maximal-eigenvalue eigenspace of φ = H m † H m - N m /N e H e † H e where H m and H e denote the channel matrices associated with the legitimate receiver and eavesdropper, respectively, and N m and N e are the noise variances at the receiver and eavesdropper, respectively. Energy efficiency is analyzed by finding the minimum bit energy required for secure and reliable communications, and the wideband slope. Increased bit energy requirements under secrecy constraints are quantified. Finally, the impact of fading is investigated, and the benefits of fading in terms of energy efficiency are shown.