Abstract
Wire-tap channels are able to provide perfect secrecy when a receiver exhibits a better channel than its wire-tapping opponent. In this letter, we extend the perfect secrecy principle to parallel Gaussian multiple input multiple output (MIMO) wire-tap channels with independent sub-channels. Assuming N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≥ N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> ≥ N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> , mathematical derivations show that a sub-optimal solution can be given in closed-form considering either secrecy rate maximization subject to a total power constraint or power minimization subject to a secrecy rate constraint. Although sub-optimal for MIMO systems, simulation results show that the proposed algorithm allows to reach higher secrecy rates with substantial gains in power consumption compared to the single input single output (SISO) system.
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