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Three novel linewidth-tolerant, low-complexity, two-stage feed-forward carrier phase estimation algorithms are introduced for dual-polarization 16-ary quadrature amplitude modulation (DP 16-QAM) with coherent detection. The first stage employs either the quadrature phase-shift keying (QPSK) partitioning algorithm, simplified QPSK partitioning algorithm, or blind phase search (BPS) algorithm. The second stage employs a novel modified QPSK partitioning algorithm. Based on experimental data, all three algorithms achieve comparable performance for DP 16-QAM back to back and transmission systems. The linewidth tolerance for the three algorithms is numerically studied. A linewidth symbol duration product of 1.3×10-4 is demonstrated for a 1 dB optical signal-to-noise-ratio penalty at a bit error ratio 10-3 of for all the proposed algorithms, which is comparable to the single-stage BPS algorithm with a large number of test phases. Reductions in the hardware complexity by factors of about 1.7-5.3 are achieved in comparison to the single-stage BPS algorithm.