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The influence of the inter-core crosstalk (ICXT) on the performance of weakly-coupled multi-core fiber (WC-MCF) systems with coherent detection and arbitrary inter-core skew is studied numerically and analytically. We analyze the evolution of the instantaneous ICXT power, induced by polarization division multiplexed quadrature amplitude modulation signals, short term average crosstalk (STAXT), and detected ICXT components along the time to get insight on how the ICXT affects the coherent system performance. Numerical results show that, with low skewsymbol rate product ( 1), the STAXT can have large fluctuations along the time and the variance of the detected ICXT can also have large fluctuations along the time, causing large variations of the bit error rate (BER) along time. With large skew-symbol rate product ( 1), the STAXT is almost constant along the time and, although the detected ICXT varies along time, the detected ICXT variance is almost constant along time leading to very small fluctuations of BER along time. Analytical expressions for the variance of the coherently detected ICXT, average BER and optical signal-to-noise ratio (OSNR) penalty are proposed and shown to agree with Monte-Carlo simulation results for arbitrary skew, modulation format order and roll-off factor of the transmitted signals. Numerical results show that the maximum allowable ICXT level for 1 dB OSNR penalty increases when the skew augments and can reach 1.3 dB for a roll-off factor of 1. For most cases of interest of low roll-off factor, the increase of the maximum allowable ICXT level is very small. It is shown that the OSNR penalty estimates agree quite well with other authors' experimental results (with nearly zero roll-off factor).

We assess, through numerical simulation, the dependence of the variance of the inter-core crosstalk (ICXT) and the maximum allowable ICXT level on the design parameters of coherent detection MCF systems. The analysed design parameters are the order of the quadrature amplitude modulation (QAM) signals, roll-off factor, time misalignment between the signal in different cores and skew between cores. The results show that, when the rolloff factor is 0, the maximum allowable ICXT level is independent of the skew and decreases for higher QAM orders. For a roll-off factor of 1, the maximum allowable ICXT level depends on the skew and time misalignment of core signals. In this case, the maximum allowable ICXT level increases by 3.6 dB relative to the case of rolloff factor of 0 with null skew, and by 2 dB, when the skew is much higher than the symbol period.

An analytical tool based on the moment generating function of the receiver decision variable that can evaluate the impact of multiple in-band crosstalk signals in DP-QPSK (Dual-Polarization Quadrature Phase-Shift Keying) signals is presented. It is shown that when the number of interferers increases from 1 to 64 the crosstalk level, that assure a 2dB power penalty, becomes more stringent, -12 dB for the single interferer scenario and -15 dB for 64 interferers. The Gaussian approximation is also used for comparison purposes.