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Quadrature phase-shift keying (QPSK) is attractive to increase transmission lengths and capacity, especially when it is combined with polarization division multiplex. Baseband processing at the symbol rate allows to keep the required electronic bandwidth low. So far, external cavity lasers seemed to be indispensable for such transmission systems due to linewidth requirements. We propose a feedforward carrier recovery scheme based on regenerative intradyne frequency dividers, i.e., the well-known regenerative frequency divider is extended to process baseband in-phase and quadrature (I and Q) signals. An IF linewidth tolerance of up to 0.001 times the QPSK symbol rate is predicted, 2 decades more than for an optical phase locked loop with a realistic loop delay. This means that commercially available DFB lasers shall suffice for synchronous optical QPSK/BPSK transmission.