  In this paper, we consider the problem of joint transmit precoding (TPC)
matrix and receive filter matrix design subject to both secrecy and
per-transmitter power constraints in the MIMO interference channel, where $K$
legitimate transmitter-receiver pairs communicate in the presence of an
external eavesdropper. Explicitly, we jointly design the TPC and receive filter
matrices based on the minimum total mean-squared error (MT-MSE) criterion under
a given and feasible information-theoretic degrees of freedom. More
specifically, we formulate this problem by minimizing the total MSEs of the
signals communicated between the legitimate transmitter-receiver pairs, whilst
ensuring that the MSE of the signals decoded by the eavesdropper remains higher
than a certain threshold. We demonstrate that the joint design of the TPC and
receive filter matrices subject to both secrecy and transmit power constraints
can be accomplished by an efficient iterative distributed algorithm. The
convergence of the proposed iterative algorithm is characterized as well.
Furthermore, the performance of the proposed algorithm, including both its
secrecy rate and MSE, is characterized with the aid of numerical results. We
demonstrate that the proposed algorithm outperforms the traditional
interference alignment (IA) algorithm in terms of both the achievable secrecy
rate and the MSE. As a benefit, secure communications can be guaranteed by the
proposed algorithm for the MIMO interference channel even in the presence of a
"sophisticated/strong" eavesdropper, whose number of antennas is much higher
than that of each legitimate transmitter and receiver.
