A Tight Lower Bound on the Gaussian Q-Function With a Simple Inversion Algorithm, and an Application to Coherent Optical Communications

We derive a tight, single-term, purely exponential, lower bound on the Gaussian Q-function, along with a method to optimize its tightness and a fast iterative method for its inversion. To illustrate its application, we show that it enables the accurate, analytical estimation of the signal-to-noise ratio penalty and the laser linewidth tolerance of coherent optical communication systems, without any time-consuming simulations.