On Secrecy Capacity of Fast Fading MIMOME Wiretap Channels with Statistical CSIT

• Published in: IEEE transactions on wireless communications Vol. 13; no. 6; pp. 3293 - 3306
• Main Authors: Lin, Shih-Chun, Lin, Cheng-Liang
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Antennas; Applied sciences; Channels; Codes; Degradation; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fading; Information, signal and communications theory; Mathematical analysis; MIMO; Optimization; partial CSIT; Radiocommunications; Receivers; Receivers & amplifiers; Receiving antennas; Secrecy capacity; Secret; Signal and communications theory; Signal to noise ratio; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Transmitting antennas; Wireless communication; Fading channels; MIMO system; Parameter estimation; partial CSIT; Transmitter; Ergodicity; Covariance matrix; Stochastic method; Optimization; Eavesdropping; Upper bound; Transmitting antenna; Channel estimation; S matrix; MIMO; Secrecy capacity; Receiving antenna; Secrecy; Antenna array; Telecommunication security; Signal to noise ratio
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2014.041714.11654

In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the antennas at the legitimate receiver are more than (or equal to) those at the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to be the same as the eavesdropper's channel matrix. Next, under the total power constraint over all transmit antennas, we analytically solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, thanks to the proposed degraded channel, we can transform the stochastic MIMOME optimization problem to be a Schur-concave one and then find its solution. Besides total power constraint, we also investigate the secrecy capacity when the transmitter is subject to the practical per-antenna power constraint. The corresponding optimization problem is even more difficult since it is not Schur-concave. Under the two power constraints considered, the corresponding MIMOME secrecy capacities can both scale with the signal-to-noise ratios (SNR) when the difference between numbers of antennas at legitimate receiver and eavesdropper are large enough. However, when the legitimate receiver and eavesdropper have a single antenna each, such SNR scalings do not exist for both cases.