# Robust Computation of Error Vector Magnitude based on Wireless Standards

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### Abstract

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 whereas the local method is a Newton method with backtracking
based on analytically derived gradient vector and Hessian matrix. A
number of test cases are shown to illustrate the concepts. A software
toolbox has been developed and is freely available.

For help, see readme.m, or run runme.m in Matlab.

*Paper published in IEEE Transactions on Communications, 2013.*

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4GMCT (VBN)

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