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This paper proposes a new behavioral model to treat memory effects in nonlinear power amplifiers (PAs). Phenomena such as asymmetries in lower and upper intermodulation terms, and variation of AM/AM and AM/PM, depending on signal history, are often observed in high-power PAs. To treat these phenomena, this paper presents a model based on the previously developed memory polynomial model. The contribution made in this paper is to augment the memory polynomial model to include a sparse delay tap structure that reduces the parameter space required for accurate model identification. A figure-of-merit, called the memory effect ratio, is defined to quantify the relative level of distortion due to memory effects, as compared to the memoryless portion. Another figure-of-merit is defined as the memory effect modeling ratio, which quantifies the degree to which the PA memory effects have been accounted for in the model. This new technique is validated using a variety of RF PAs, including an 880-MHz and a 2.1-GHz high-power laterally diffused metal-oxide semiconductor PA and various signals such as two-tone, eight-tone, and IS-95B signals.