  This paper investigates a new class of non-convex optimization, which
provides a unified framework for linear precoding in single/multi-user
multiple-input multiple-output (MIMO) channels with arbitrary input
distributions. The new optimization is called generalized quadratic matrix
programming (GQMP). Due to the nondeterministic polynomial time (NP)-hardness
of GQMP problems, instead of seeking globally optimal solutions, we propose an
efficient algorithm which is guaranteed to converge to a Karush-Kuhn-Tucker
(KKT) point. The idea behind this algorithm is to construct explicit concave
lower bounds for non-convex objective and constraint functions, and then solve
a sequence of concave maximization problems until convergence. In terms of
application, we consider a downlink underlay secure cognitive radio (CR)
network, where each node has multiple antennas. We design linear precoders to
maximize the average secrecy (sum) rate with finite-alphabet inputs and
statistical channel state information (CSI) at the transmitter. The precoding
problems under secure multicast/broadcast scenarios are GQMP problems, and thus
they can be solved efficiently by our proposed algorithm. Several numerical
examples are provided to show the efficacy of our algorithm.
