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The impact from phase drifts in the different branches of parallel coherent receivers is investigated and it is shown how the spectrum is broadened when the receiver branches are not phase stabilized. Based on this, we propose a blind algorithm for compensating these phase drifts in digital signal processing by minimization of the spectral width. The algorithm performance is then evaluated by numerical simulations of quadrature phase-shift keying data using return-to-zero modulation. It is found that the algorithm is capable of identifying the phases with sufficient accuracy to make the residual effect of the phase mismatches negligible compared to the signal distortion by noise at a bit error rate of 10-3.