Performing blind calibration is highly important in modern sensing strategies, particularly when calibration aided by multiple, accurately designed training signals is infeasible or resource-consuming. We here address it as a naturally-formulated non-convex problem for a linear model with sub-Gaussian ran- dom sensing vectors in which both the sensor gains and the sig- nal are unknown. A sample complexity bound is derived to as- sess that solving the problem by projected gradient descent with a suitable initialisation provably converges to the global optimum. These findings are supported by numerical evidence on the phase transition of blind calibration and by an imaging example.