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In a previous paper , we noted when the transmitted signal constellations has rotational symmetry, laser phase noise can be mitigated using non-data-aided (NDA) feedforward (FF) carrier recovery. The structures of a FF carrier recovery unit and a NDA soft-decision phase estimator were shown in Fig. 3 and 4(a), respectively. We have found that in an NDA FF carrier recovery unit, the order of the linear filter and phase estimator can be exchanged in a manner not possible with a decision-directed (DD) FF carrier recovery unit. We show that this alternative NDA (ANDA) FF carrier recovery unit exhibits better immunity to cycle slips compared to standard NDA.