Optimal MISO secrecy beamforming via quasi-convex programming with rank-one transmit covariance guarantee

Authors:
Ling Tang;Hao Liu;Jianhui Wu
Affiliations:
Southeast University, Nanjing, China;Southeast University, Nanjing, China;Southeast University, Nanjing, China
Venue:
Proceedings of the 6th International Wireless Communications and Mobile Computing Conference
Year:
2010

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Abstract

This paper studies the secrecy capacity of the multiple input single output (MISO) secrecy channel where a transmitter is communicating to a receiver in the presence of K eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each has a single antenna. The transmitter maximizes the communication rate, while concealing the message from all the eavesdroppers. It is known that the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the mutual information of the secrecy user channel and those of the eavesdroppers channels. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently. This paper proposes an efficient algorithm based on quasi-convex programming, which not only leads to the optimal transmit covariance matrix, but also guarantees that it is always rank-one at any search step with finite accuracy. Such a guaranteed rank-one covariance matrix is critical to practical implementations of MISO secrecy transmission beam-forming.