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We numerically and analytically calculate sensitivity and link power budget of an optically amplified electronically compensated dual polarization quadrature phase-shift keying (DP-QPSK) coherent homodyne optical system, taking into account the main parameters of both the optical amplifier and the coherent receiver. After deriving an expression for the signal-to-noise ratio (SNR) of the amplified coherent receiver, we calculate an analytical expression for the optimum local oscillator (LO) optical power which maximizes the SNR, and an approximated closed-form solution for the receiver sensitivity, valid in most of practical cases. This analytical calculation allows to derive, when the impairments of the fiber are compensated, the position of the amplifier into the link that maximizes the optical link power budget. The approximated closed-form solutions are compared with results obtained with a numerical approach. From our investigation it emerges that, in a single-channel fully compensated DP-QPSK coherent system, the performances of both booster and in-line configurations can be even better than that ones of the preamplifier, but they are strongly dependent on the unamplified receiver features, and can require a proper adjustment of the LO optical power, to make the sensitivity compliant with the requirements. Diversely, the performances of a preamplified coherent receiver can be worse, but the amplifier position makes the coherent receiver practically independent on its intrinsic noise sources.