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This paper investigates the linear pre-coder design for spectrum sharing in multi-antenna cognitive radio networks with finite alphabet inputs. It formulates the pre-coding problem by maximizing the constellation constrained mutual information between the secondary user transmitter and secondary user receiver while controlling the interference power to primary user receivers. This formulation leads to a nonlinear and nonconvex problem, presenting a major barrier to obtain optimal solutions. This paper proposes a global optimization algorithm, namely Branch and bound Aided Mutual Information Optimization (BAMIO) that solves the pre-coding problem with arbitrary prescribed tolerance.
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