## 1 Introduction  
The evolution of communication networks is driven by the development and deployment of the 5 th generation wireless networks (5G) [1]. The observed trends result in the increase in metro, cloud and data center traffic, broadband speed, and numbers of devices connected to the Internet. In this context, optical fiber networks are considered a key technology for building the underlying transport infrastructure capable of assuring high capacity, good scalability, low latency, carrier-class reliability, and adaptability to rapidly changing demand and traffic patterns for best resource utilization. Spatially and spectrally flexible optical networks, which combine space division multiplexing (SDM) [2] with flexible-grid elastic optical network (EON) technologies [3], have been proposed as a long-term solution for ever-increasing capacity requirements in optical networks [4, 5]. SDM allows for the parallel transmission of a number of spatial modes in suitable designed optical fibers, such as weakly coupled multi-core fibers [6]. Concurrently, EONs enable a multi-carrier (super-channel, SCh), distance-adaptive transmission of optical signals using flexibly assigned spectrum resources according to their demands [7]. In SS-FONs, lightpath connections are established using both spatial and spectral resources available in SDM links. A lightpath carries an SCh, which represents a bundle of optical signals transmitted using adjacent optical carriers within an appropriately allocated spectrum (frequency) slot. The lightpaths are routed between their source and destination nodes over the assigned spatial modes of SDM links. The allocation of frequency slots on spatial modes to particular lightpaths should be contention-free; i.e., any two lightpathscannot have assigned an overlapping segment of spectrum if they are routed through the same spatial mode over the same SDM link. The corresponding transmission resource allocation problem is called the routing, spatial mode and spectrum allocation (RSSA) problem [8]. One of the main issues in the operation of MCF-based SS-FONs is the degradation of signal quality of lightpaths due to the inter-core crosstalk effect that occurs in the MCFs [9]. In particular, the XT impairment affects the optical signals transmitted in an overlapping segment of spectrum in adjacent MCF cores. If the degradation is too high, the signals cannot be received properly. Therefore, the impact of XT on transmission quality should be accounted for when provisioning lightpaths in the SS-FONs connected using MCFs. In this paper, we address the classical problem of planning of lightpath connections for a set of end-to-end traffic demands with a goal to optimize the utilization of spectral-spatial resources in MCF-based SS-FONs. The main novelty of this work is the application in network optimization of a reliable OSNR-based QoT estimation model [10], in which XT is considered as yet another source of the OSNR degradation, along with other physical-layer impairments (PLIs). The use of this model improves the accuracy of QoT estimation when compared to prior works concerning the optimization of SS-FONs, in which XT was considered either as the only source of signal degradation (e.g., see [11, 12]), or it was treated independently from other PLIs (e.g., see [13, 14]). To model the optimization problem considered, we propose a novel MIP formulation that incorporates the OSNR-based estimator as a set of problem variables and constraints. By solving MIP in different XT scenarios, we show that the use of the OSNR model complicates significantly the lightpath planning problem, which itself (i.e., without QoT awareness) is \(\mathcal{NP}\)-hard [8]. Therefore, to provide solutions to larger problem instances, we propose an efficient heuristic method. As numerical results show, the heuristic is capable of generating good-quality solutions to the optimization problem. The main contributions of this work are the following:  
1.