In this paper, we consider the problem of power allocation in MIMO wiretapchannel for secrecy in the presence of multiple eavesdroppers. Perfectknowledge of the destination channel state information (CSI) and only thestatistical knowledge of the eavesdroppers CSI are assumed. We first considerthe MIMO wiretap channel with Gaussian input. Using Jensen's inequality, wetransform the secrecy rate max-min optimization problem to a singlemaximization problem. We use generalized singular value decomposition andtransform the problem to a concave maximization problem which maximizes the sumsecrecy rate of scalar wiretap channels subject to linear constraints on thetransmit covariance matrix. We then consider the MIMO wiretap channel withfinite-alphabet input. We show that the transmit covariance matrix obtained forthe case of Gaussian input, when used in the MIMO wiretap channel withfinite-alphabet input, can lead to zero secrecy rate at high transmit powers.We then propose a power allocation scheme with an additional power constraintwhich alleviates this secrecy rate loss problem, and gives non-zero secrecyrates at high transmit powers.
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