On the finite-SNR diversity-multiplexing tradeoff of zero-forcing transmit scheme under secrecy constraint

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IEEE International Conference on Communications, ISSN: 0536-1486, Page: 1-5

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Rezki, Zouheir; Alouini, Mohamed-Slim
Institute of Electrical and Electronics Engineers (IEEE); Institute of Electrical and Electronics Engineers
Computer Science; Engineering; Diversity-Multiplexing tradeoff; Finite-SNR; MIMO wiretap; secrecy capacity; secret outage probability; Zero-Forcing transmit scheme
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In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secret multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secret diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secret diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secret diversity gain of the Multiple-Input Multiple-Output (MIMO) wiretap channel. © 2011 IEEE.