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This paper proposes a Volterra kernel identification procedure for wireless amplifiers with nonlinear memory. The technique is based on a reduced-order Volterra model for wideband amplifiers that is favorably compared with widely used memory polynomial model in terms of normalized mean square error. The identification method takes advantage of the particular model structure and is thoroughly derived with a proper selection of pulse-like waveforms of known amplitude as probing signals with special emphasis on the extraction of the fifth-order kernel. The main advantage of the method is that it allows exploring the dynamic range of the amplifier without rising the temperature in the device or altering the biasing point. For validation purposes, a commercial amplifier has been characterized and the extracted kernels have been used to predict the response under wideband code-division multiple-access-like signals. In addition to the simplicity of the deterministic approach used in this extraction procedure, the agreement of the predicted responses with measurements was highly satisfactory in all cases and permitted the capture of phenomena that are due to nonlinear memory effects.