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.

[1]  G. William Walster,et al.  Global Optimization Using Interval Analysis: Revised and Expanded , 2007 .

[2]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[3]  Ruifeng Liu,et al.  EVM estimation by analyzing transmitter imperfections mathematically and graphically , 2006 .

[4]  Xiaoli Ma,et al.  Error Vector Magnitude Optimization for OFDM Systems With a Deterministic Peak-to-Average Power Ratio Constraint , 2009, IEEE Journal of Selected Topics in Signal Processing.

[5]  Izzat Darwazeh,et al.  Error vector magnitude relation to magnitude and phase distortion in 8-PSK systems , 2001 .

[6]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[7]  Horst Reiner,et al.  Introduction to Global Optimization. Second Edition , 2000 .

[8]  R. Hassun,et al.  Effective evaluation of link quality using error vector magnitude techniques , 1997, Proceedings of 1997 Wireless Communications Conference.

[9]  Ashkan Mashhour,et al.  A method for computing error vector magnitude in GSM EDGE systems-simulation results , 2001, IEEE Communications Letters.

[10]  Zhe Xu,et al.  Key Algorithms for Accurate GSM EDGE EVM Measurement on ATE Platform , 2006, 2006 8th International Conference on Solid-State and Integrated Circuit Technology Proceedings.

[11]  Apostolos Georgiadis,et al.  Gain, phase imbalance, and phase noise effects on error vector magnitude , 2004, IEEE Transactions on Vehicular Technology.

[12]  Hüseyin Arslan,et al.  Error vector magnitude to SNR conversion for nondata-aided receivers , 2009, IEEE Transactions on Wireless Communications.

[13]  Jelena Kovacevic,et al.  Reproducible research in signal processing , 2009, IEEE Signal Process. Mag..

[14]  A. Bateman,et al.  Adjacent channel power and error-vector magnitude performance of reduced complexity CALLUM systems , 1999 .

[15]  R. Quere,et al.  Joint optimization of the power-added efficiency and the error-vector measurement of 20-GHz pHEMT amplifier through a new dynamic bias-control method , 2004, IEEE Transactions on Microwave Theory and Techniques.

[16]  Christodoulos A. Floudas.  Generalized Benders Decomposition , 2009, Encyclopedia of Optimization.

[17]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[18]  Kazuaki Kunihiro,et al.  An efficient algorithm for simulating error vector magnitude in nonlinear OFDM amplifiers , 2004, Proceedings of the IEEE 2004 Custom Integrated Circuits Conference (IEEE Cat. No.04CH37571).

[19]  Michel C. Jeruchim,et al.  Simulation of Communication Systems: Modeling, Methodology and Techniques , 2000 .

[20]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[21]  R.A. Shafik,et al.  On the Extended Relationships Among EVM, BER and SNR as Performance Metrics , 2006, 2006 International Conference on Electrical and Computer Engineering.

[22]  E. Acar,et al.  Enhanced Error Vector Magnitude (EVM) Measurements for Testing WLAN Transceivers , 2006, 2006 IEEE/ACM International Conference on Computer Aided Design.

[23]  Dominique Schreurs,et al.  RF Power Amplifier Behavioral Modeling: Contents , 2008 .

[24]  J.S. Kenney,et al.  Estimation of error vector magnitude using two-tone intermodulation distortion measurements [power amplifier] , 2001, 2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157).

[25]  Torben Larsen,et al.  On wafer X-parameter based modeling of a switching cascode power amplifier , 2011, 2011 NORCHIP.

[26]  Leo Liberti,et al.  Introduction to Global Optimization , 2006 .

[27]  Panos M. Pardalos,et al.  Introduction to Global Optimization , 2000, Introduction to Global Optimization.

[28]  S. Freisleben.  Semi-analytical computation of error vector magnitude for UMTS SAW filters , 2002, 2002 IEEE Ultrasonics Symposium, 2002. Proceedings..

[29]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[30]  Simon Haykin,et al.  Adaptive Filter Theory 4th Edition , 2002 .

[31]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[32]  Maciej Myslinski,et al.  EVM Calculation for Broadband Modulated Signals , 2004 .