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This paper investigates the interference-aware linear precoder design with finite-alphabet inputs. It maximizes the mutual information between the transmitter and intended receiver while controlling the interference power caused to unintended receivers. For this nonconcave problem, this work proposes a global optimization approach, which is based on two key observations: 1) the interference-aware precoding problem can be reformulated to the problem minimizing a function with bilinear terms over the intersection of multiple co-centered ellipsoids; 2) these bilinear terms can be relaxed by their convex and concave envelopes. In this way, the global optimal solution is obtained by solving a sequence of relaxed problems over shrinking feasible regions. The proposed algorithm calculates the optimal precoder and the theoretical limit of the transmission rate with interference constraints. Thus, it offers an important benchmark for performance evaluation of interference constrained networks.