# Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems
## 1 Introduction  
In the past few years, coherent communication techniques have established themselves as the main solution to overcome the capacity limitations of legacy intensity modulation/direct detection (IM-DD) systems in optical communications [1]. The feasibility of coherent optical communications came with advances in silicon technology that allowed the full mitigation and compensation of linear transmission impairments by digital signal processing (DSP) [2]. In such systems, the data need to be processed synchronously. Sending a pilot clock tone together with the signal through the optical fiber would be inefficient, raising the need for extraction of the clock information from the data waveform itself. Channel impairments and transceiver imperfections such as chromatic dispersion (CD), polarization mode dispersion (PMD) and time skew between components were shown to be critical for clock extraction [3; 4; 5; 6; 7], making analog clock recovery unfeasible. Thus, to partially compensate these impairments before a fully digital clock recovery is mandatory. The first implementations of DSP-based coherent optical receivers were deployed envisioning systems with 100 Gb/s per channel over single-mode fibers (SMF), and employing polarization division multiplexing (PDM) and advanced modulation formats such as \(m\)-ary phase-shift keying (\(M\)-PSK) and \(m\)-ary quadrature amplitude modulation (\(M\)-QAM) [2; 8]. Such systems in combination with wavelength division multiplexing (WDM) can not satisfy future capacity demands. One of the most promising options for overcoming the capacity bottleneck is to employ space division multiplexing (SDM) [1]. SDM is an enabling technology that can provide interface data rates for future 10 Tb/s per channel and beyond systems [9; 10]. It can be realized by multiplexing the signal in several cores using multicore fibers (MCF) as the transmission channel, several modes using few mode fibers (FMF), also known as mode division multiplexing (MDM) or by a combination of the two. For systems employing MCF, a relatively low degree of crosstalk between cores can be achieved. In contrast, this is a challenging task for systems employing FMF, where a high degree of mode crosstalk may occur [11]. So far, the research community has mainly focused on equalization schemes for mode mixing and delay spread mitigation [12; 13; 14; 15; 16; 17; 18]. Strong mode coupling regime has been shown to be preferable in terms of equalizer impulse response length [11] and nonlinearity tolerance [19; 20]. However, most experimental demonstrations have been in the weak/intermediate coupling regimes [12]. So far, very little attention has been paid to the impact of mode mixing on clock recovery performance and feasibility. Typically, clock recovery is performed before dynamic multiple-input multiple-output (MIMO) equalization by extracting a clock tone from the signal and then resampling it, so if the clock tone cannot be extracted due to transmission impairments, the remaining part of the DSP chain may fail [5]. It is therefore essential to investigate the tolerance and performance of clock recovery for systems employing MDM. In this article, we extend our recent work [21] and present a detailed numerical analysis of clock recovery for long-haul transmission dual-polarization in a SMF and space-division multiplexing using a FMF in weak, intermediate and strong coupling regimes. We show that although for a SMF, the clock tone vanishing can be dealt with a simple polarization rotation [7] and compensation of the transmitter time-skew between polarizations [22], the combined effects of mode coupling and inter-modal dispersion in a FMF can significantly degrade the performance of the timing synchronization. In the strong coupling regime, even with low group delay spread, the clock tone completely vanishes, making timing synchronization challenging. This article is structured as follows. In Section 2, we present a review of clock recovery in coherent optical receivers, showing the basic algorithm implementations.