Summary: We numerically investigate a PDM-QPSK multi-rate coherent burst-mode optical receiver capable of receiving 3 different line-rates, suitable for next generation optical networks such as hybrid optical circuit switching (OCS)/optical packet switching (OPS) networks, access networks and datacenter networks. The line-rate detection algorithm relies on a simple-to-generate optical header, it is based on the fast Fourier transform (FFT) which can be efficiently implemented with the Goertzel algorithm, and it is insensitive to polarization rotations and frequency offset. Numerically, we demonstrate that performance in terms of packet detection rate (PER) can be tailored by controlling the sizes of the packet header and the line-rate estimator.