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Abstract: Based on expanded memory polynomial (EMP) and orthogonal EMP (OEMP), this paper addresses the nonlinear system identification (NSI) problem by introducing an amplitudephase-frequency (APF) characterization framework to enable performance measurability, monotonicity, and optimality. APF characteristic functions (CFs) are defined to better capture the nonlinear distortions arising from both the amplitude and phase of the input signal. It is shown that an APF CF can be expressed as a weighted sum of characteristic basis functions (CBFs) or their orthogonal counterparts (OCBFs), with the associated CBF or OCBF frequency responses directly linked to the EMP or OEMP coefficients. As a result, NSI can be carried out by alternatively estimating the CBF or OCBF frequency responses. The paper also presents detailed estimation methods employing frequency modulated continuous wave (FMCW) test signals and analyzes different mean-squared-error (MSE) measurement strategies. Simulation and experimental results using a 73.5 GHz carrier frequency and 2.125 GHz bandwidth millimeter wave communication system validate the effectiveness and practical applicability of the proposed technique.