We present an overview on a recently developedtechnique for performing antenna gain measurements with gainextrapolation that uses significantly fewer data points and atshorter distances than traditional gain extrapolation. This enhancedtechnique purposely incorporates third-order mutualcoupling between antennas, which can be thought of as a usefulhomodyne signal, rather than an unwanted degradation of theantenna-to-antenna coupling signal as has been the historicallyaccepted viewpoint. From Wacker’s fundamental extrapolationequations, we give the development of the third-order signalwhich underpins this technique. From the third-order signal theframing of gain extrapolation can be approached as a measureof interference fringes, as opposed to a by-rote curve fittingproblem, and thus provides ways of specifying the numberof required data points and measurement distances so as toreduce both significantly from the traditional gain extrapolationapproach. The truncation order of the full signal expansion,as it relates to the conditioning of the problem, is presentedin light of the behavior of the design matrix that defines thegain extrapolation scenario and the orders of scattering, thusleading to fewer required samples. Along with considerations ofthe matrix conditioning, guidelines are presented from the thirdordersignal and interference fringes for sampling criteria andsampling accuracy criteria. These aid in choices of measurementsystem accuracy and precision requirements based on knownvalues of the operating frequency, wavelength, and antennadimensions. Bounds for gain uncertainty based on these samplingcriteria are also given. Results comparing NIST reference antennameasurements made with the traditional gain extrapolationand enhanced gain extrapolation technique are presented. It isshown that the enhanced technique can produce gain values inagreement and within uncertainties of the traditional techniquefor the reference antennas.