Signalling and Resource Allocation for Secure Communication in Gaussian Wireless Channels
ProQuest, 2008 - 111 pages
For the passive eavesdropping attack, we study multiple-input multiple-output (MIMO) AWGN channels. We first consider a multiple-input single-output (MISO) channel, where the transmitter has multiple antennas, while the receiver and the eavesdropper have single antennas each. We find achievable rates for this channel. With the channel input restricted to Gaussian signalling with no pre-processing of information, optimal transmission strategies that maximize the achievable secrecy rates are found, in terms of the input covariance matrices. It is shown that, under the optimal communication strategy, the system reduces to a single-input single-output (SISO) channel. We then extend the achievability results to fading Gaussian MISO channels. Finally, as a step toward generalizing the problem to one with multiple antennas at the receiver, we discuss the Gaussian 2-2-1 channel with a transmitter and a receiver with two antennas each, and a single antenna eavesdropper. We develop an achievability scheme similar to those of the SISO and MISO channels, and further show that in fact, it achieves the secrecy capacity of this 2-2-1 channel.
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achievable scheme achievable secrecy rates assume AWGN beam-forming best response channel attenuations channel experiences fading characterize chooses its strategy complementary slackness variable concave function convex function correlated jamming covariance matrix deﬁned diﬀerent eavesdropping channel eavesdropping information eigenvalue fading channels fading level feasible jamming signals ﬁnd ﬁxed game solution Gaussian MISO channel Gaussian noise Gaussian random variables Gaussian signalling hP(h input/output mutual information jammer best response jammer knows jammer power allocation jamming strategy jamming with CSI KKTs Lemma linear jammer linear jamming signal matrix inversion lemma maximizes non-fading optimization problem pair of user Pi(h power allocation strategies pre-processing of information rate achievable Rayleigh quotient received signal saddle point solution secrecy capacity signalling scheme single-user SISO speciﬁc sub-channel transmitted signal uncorrelated unit-rank upper bound user and jammer user channel user power allocation user signals user transmits user’s vector wire-tap channel X1 and X2