###### Abstract  
This paper proposes and evaluates the use of machine learning (ML) techniques for mitigating the effect of the random inter-core crosstalk (ICXT) on 256 Gb/s short-reach systems employing weakly coupled multicore fiber (MCF) and Kramers-Kronig (KK) receivers. The performance improvement provided by the \(k\)-means clustering, \(k\) nearest neighbor (KNN) and feedforward neural network (FNN) techniques are assessed and compared with the system performance obtained without employing ML. The FNN proves to significantly improve the system performance by mitigating the impact of the ICXT on the received signal. This is achieved by employing only 10 neurons in the hidden layer and four input features for the training phase. It has been shown that \(k\)-means or KNN techniques do not provide performance improvement compared to the system without using ML. These conclusions are valid for direct detection MCF-based short-reach systems with the product between the skew (relative time delay between cores) and the symbol rate much lower than one (\(skew\times symbol\ rate\ll 1\)). By employing the proposed FNN, the bit error rate (BER) always stood below \(10^{-1.8}\) on all the time fractions under analysis (compared with 100 out of 626 occurrences above the BER threshold when ML was not used). For the BER threshold of \(10^{-1.8}\) and compared with the standard system operating without employing ML techniques, the system operating with the proposed FNN shows a received optical power improvement of almost 3 dB.  
short-reach systems; multicore fiber; machine learning; Kramers-Kronig receiver +
Footnote †: journal: _Photonics_  
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limit the achievable capacity and reach. Thus, advanced DD receivers based on Kramers-Kronig (KK) technique have been proposed for performance improvement and complexity reduction compared with coherent detection counterpart [10]. With the KK technique, linearization of the receiver is attained, and the signal phase information can be recovered.  
Recently, machine learning has been employed in optical communications to recover from nonlinear distortions, including non-Gaussian additive noise, non-white laser phase noise, and fiber nonlinearities in both IM/DD and coherent systems [11; 12]. Simplest machine learning techniques include \(k\)-means and \(k\) nearest neighbor (KNN), which represent an unsupervised technique used for clustering and a supervised learning technique used for classification, respectively [13]. Feedforward neural networks (FNNs) are one of the simplest machine learning techniques where a set of perceptrons are organized into layers to form a fully connected neural network (NN). FNNs are suitable for memoryless systems and have been employed in optical fiber communications to perform equalizations, as shown in [11]. Beside FNN, more advanced NN architectures have been studied in optical communications, such as deep learning [12; 14]. These more advanced NN are used to predict different strategies for routing and spectrum assignments for elastic optical networks [14]. They can also be used to mitigate the non-linearities, such as signal-to-signal beat interference caused by the square-law detection [12]. In SDM systems, machine learning techniques were proposed to support the design of crosstalk-aware schemes used for resources allocation [15] or to mitigate the impact of the crosstalk power between mode groups in mode-multiplexed M-quadrature amplitude modulation (QAM) OFDM-IM-DD systems [16]. NNs were also used to speed up coating loss estimation in heterogeneous trench-assisted MCF design [17].  
In this work, \(k\)-means clustering and KNN, as well as a low-complexity FNN, are proposed to mitigate the effects of the random variation of the ICXT along time, induced by weakly coupled MCF in short-reach systems employing KK receivers.