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This paper presents a novel digital feedforward carrier recovery algorithm for arbitrary M-ary quadrature amplitude modulation (M-QAM) constellations in an intradyne coherent optical receiver. The approach does not contain any feedback loop and is therefore highly tolerant against laser phase noise. This is crucial, especially for higher order QAM constellations, which inherently have a smaller phase noise tolerance due to the lower spacing between adjacent constellation points. In addition to the mathematical description of the proposed carrier recovery algorithm also a possible hardware-efficient implementation in a parallelized system is presented and the performance of the algorithm is evaluated by Monte Carlo simulations for square 4-QAM (QPSK), 16-QAM, 64-QAM, and 256-QAM. For the simulations ASE noise and laser phase noise are considered as well as analog-to-digital converter (ADC) and internal resolution effects. For a 1 dB penalty at BER = 10-3, linewidth times symbol duration products of 4.1 x 10-4 (4-QAM), 1.4 x 10-4 (16-QAM), 4.0 x 10-5 (64-QAM) and 8.0 x 10-6 (256-QAM) are tolerable.