  In this paper, we propose two secure multiuser multiple-input multiple-output
transmission approaches based on interference alignment (IA) in the presence of
an eavesdropper. To deal with the information leakage to the eavesdropper as
well as the interference signals from undesired transmitters (Txs) at desired
receivers (Rxs), our approaches aim to design the transmit precoding and
receive subspace matrices to minimize both the total inter-main-link
interference and the wiretapped signals (WSs). The first proposed IA scheme
focuses on aligning the WSs into proper subspaces while the second one imposes
a new structure on the precoding matrices to force the WSs to zero. When the
channel state information is perfectly known at all Txs, in each proposed IA
scheme, the precoding matrices at Txs and the receive subspaces at Rxs or the
eavesdropper are alternatively selected to minimize the cost function of an
convex optimization problem for every iteration. We provide the feasible
conditions and the proofs of convergence for both IA approaches. The simulation
results indicate that our two IA approaches outperform the conventional IA
algorithm in terms of average secrecy sum rate.
