This paper addresses information-maximizing sensor selection that determines a set of measurement locations providing the largest entropy reduction in the estimates of the state variables. A new mixed-integer semidefinite program (MISDP) formulation is proposed for this selection under the constraints resulting from communication limitations. This formulation employs binary variables indicating if the corresponding measurement location is selected, and ensures convexity of the objective function and linearity of the constraint functions by exploiting the linear equivalent form of a bilinear term involving binary variables. An outer-approximation algorithm is then developed for the MISDP formulation that obtains the global optimal solution by solving a sequence of mixed-integer linear programs for which reliable solvers are available. Numerical experiments verify the solution optimality and the computational effectiveness of the proposed algorithm by comparing it to branch-and-bound-based approaches with nonlinear programming relaxation. An example of sensor selection to track a moving target is considered to demonstrate the applicability of the proposed method and highlight its ability to handle quadratic constraints.