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mmWave wireless communication is proposed for high-throughput and high-density applications. Due to the large channel bandwidth, mmWave systems face a large variation in the observed delay spread. Many proposed single-carrier (SC) mmWave systems rely on cyclic-prefix (CP) frequency domain equalization (FDE) in order to deal with worst case channel conditions. A downside of CP-FDE receivers is their constant energy consumption independent of the actual channel conditions. The alternative overlap-save (OS) FDE receiver can adapt its complexity, but exhibits an inferior equalization performance. By proposing a hybrid FDE approach the receiver can adapt its complexity and therefor its power consumption dynamically to the given channel conditions. Using the structural similarity of overlap-save and cyclic-prefix FDE architectures the proposed hybrid receiver can switch between the two modes of operation with minimum required hardware overhead. It is shown that the proposed hybrid receiver can significantly reduce its complexity in benign channel conditions while still matching the equalization properties of a conventional CP-FDE receivers in very frequency selective environments.