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Instrumenting power networks with phasor measurement units (PMUs) facilitates several tasks including optimum power flow, system control, contingency analysis, visualization, and integration of renewable resources, thus enabling situational awareness-one of the key steps toward realizing the smart grid vision. The installation cost of PMUs currently prohibits their deployment on every bus, which in turn motivates their strategic placement across the power grid. As state estimation is at the core of grid monitoring, PMU deployment is optimized here based on estimation-theoretic criteria. Considering both voltage and incident current readings per PMU-instrumented bus and incorporating conventionally derived state estimates under the Bayesian framework, PMU placement is formulated as an optimal experimental design task. To bypass the combinatorial search involved, a convex relaxation is developed to obtain solutions with numerical optimality guarantees. In the tests performed on standard IEEE 14-, 30-, and 118-bus benchmarks, the proposed relaxation approaches and oftentimes attains the optimum PMU placement.