Gain Loss in Metasurfaces Caused by Reflection-Coefficient Quantization: An Error Vector Magnitude Approach

Metasurfaces with a finite number of discrete reflection states inevitably suffer gain loss compared with their ideal continuous-phase counterparts. This paper proposes an error vector magnitude (EVM)-based metric, denoted ΓEVM, for the complex reflection coefficient of a metasurface unit, where ΓEVM is defined as the root-mean-square difference between the ideal and realizable reflection coefficients over [0, 2𝜋). The metric enables quantitative evaluation of the unit’s quantization precision and prediction of the resulting gain loss in the entire array. Assuming a uniform phase probability density function (PDF) over [0, 2𝜋), a closed-form expression for ΓEVM is derived together with an empirical relation that relates ΓEVM to the gain loss, so that the array radiation efficiency can be estimated directly from ΓEVM. For practical metasurfaces with nonuniform phase statistics, a statistical method based on empirical phase PDFs is introduced, resulting in a closed-form expressions for the expectation and variance of the gain-loss statistics in terms of ΓEVM and the total number of metasurface units. The proposed method is validated by Monte Carlo simulations and on five 20 × 20 prototypes operating at 28 GHz and covering quantization levels from 1-bit to multiple-bit resolutions. Measurements confirm agreement with theoretical estimations, with a maximum deviation of 0.34 dB. These results demonstrate that the proposed metric provides a generalizable and easy-to-use tool for estimating metasurface gain loss, facilitating efficient design in 5G and satellite communication systems.