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We present a highly efficient carrier phase recovery module for coherent optical detection of single-carrier advanced modulation formats with differential precoding. Remarkably, we eliminate all multipliers from the multisymbol-delay-detector (MSDD) carrier recovery system, without incurring performance penalty relative to the previously shown complex-domain MSDD. We also introduce a novel polyblock hardware parallelization method for the MSDD, eliminating the “distant feedback” parallelization penalty of decision-feedback-based carrier recovery methods, such as MSDD. Simulations indicate extremely high nonlinear phase noise tolerance for the new polar MSDD carrier recovery system for 16-QAM 2000 km transmission. The ultralow-complexity CR is simulated and electrically demonstrated in real-time at 25 Gbaud symbol rate over FPGA HW for single-carrier QPSK and 16-QAM constellations, respectively.