Robust Computation of Error Vector Magnitude for Wireless Standards

The modulation accuracy described by an error vector magnitude is a critical parameter in modern communication systems — defined originally as a performance metric for transmitters but now also used in receiver design and for more general signal analysis. The modulation accuracy is a measure
of how far a test signal is from a reference signal at the symbol values when some parameters in a reconstruction model are optimized for best agreement. This paper provides an approach to computation of error vector magnitude as described in several standards from measured or simulated data. It is shown
that the error vector magnitude optimization problem is generally non-convex. Robust estimation of the initial conditions for the optimizer is suggested, which is particularly important for a non-convex problem. A Bender decomposition approach is used to separate convex and non-convex parts of the problem to make the optimization procedure simpler and robust. A two step global optimization method is suggested where the global step is the grid method and the local method is the Newton method. A number of test cases are shown to illustrate the concepts.