## 1 Introduction  
One of the main goals and challenges for telecoms and backbone optical networks operators is to provide high network throughput (amount of served traffic) in a cost-effective way. In recent years, we have been observing an evolution of optical networks from fixed-grid _wavelength division multiplexing_ (WDM) networks to flex-grid spectrally flexible _elastic optical networks_ (EONs) which allow for adaptive use of different modulation formats and multi-carrier (super-channel) transmission. Another possible step towards providing higher network throughput is using a _space division multiplexing_ (SDM) paradigm--a relatively new optical network idea that extends the capacity and capabilities of optical networks. In particular, SDM enables parallel transmissions of a number of co-propagating spatial modes in appropriately designed optical fibers. _Spectrally-spatially flexible optical networks_ (SS-FONs), which join the main features of SDM and EONs, provide numerous advantages such as substantial growth of transmission capacity, cost savings due to the use of integrated devices, and extended flexibility in resource management due to the introduction of the spatial domain (spatial modes) [1; 2; 3]. Another concept that has the capability to allow increasing network throughput are _translucent networks_. The key motivation behind translucent networks is to mitigate the limited transmission reach in optical networks by using signal regeneration to re-amplify, reshape, and retime the optical signals. Translucent optical networks are planned to account for limited transmission reach and deal with this issue by regenerating signals in selected nodes. Such networks enable a compromise between network design cost and service provisioning performance including network capacity. However, the regenerator placement becomes one of the main problems to be addressed when planning and operating the translucent networks [4]. The idea of translucent networks emerged in the context of WDM optical networks, and the key design challenge in such networks is to select regeneration nodes that allow for regeneration of WDM lightpaths. The arrival of EONs triggered a new research effort in the context of translucent networks because of the introduction of flexible frequency grids and the possibility to apply different modulation formats of different spectral efficiency and transmission reaches. In particular, in the case when the transmission distance of a particular lightpath exceeds the transmission reach of the applied modulation format, it is required to regenerate the signal. It should be mentioned that modulation formats offer a trade-off between the spectral efficiency and transmission reach, i.e., more spectrally efficient modulation formats provide shorter transmission reaches, but, at the same time, they require less spectrum resources [5]. In this work, for regeneration, we used an approach based on the application of transponders (TRXs) operating in back-to-back (B2B) configurations, i.e., with interconnections at the client side [6; 7; 8; 9; 10]. The main benefit of B2B regeneration is the fact that dedicated regenerators are not required. The optical network can be equipped only with tunable transponders that are utilized for two purposes: transmitting/receiving of the signal at the source/destination nodes (add/drop) and regeneration of the signal at some intermediate nodes. Therefore, semi-transparent (translucent) lightpath connections are established in optical networks with B2B regeneration. Moreover, according to Reference [10], the advent of elastic optical transponders allows to change the output signal modulation format during the regeneration process. This can be achieved by means of patch-cords or electronic cross-connects providing traffic interchange among several transponders. In consequence, the lightpath may consist of several transparent segments, where each segment uses a different modulation format.