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This letter presents a monolithic integration of an antenna with an array of neural recording electrodes on a flexible thin film. The structure was designed for long-term neural recording in a wireless brain-machine interface system. The implant-on-body antenna pair is optimized for maximal link power efficiency to maximize the battery life of a portable outside-body control unit. We provide guidelines for the design of the sub-skin-depth implant antenna and validate the antenna simulation model with wireless link measurements in air. We propose a new computational analysis of both the power and voltage delivery to the battery-free implant under design variations to guarantee efficient on-chip RF-to-dc conversion.