# Frequency Comb-Based WDM Transmission Systems Enabling Joint Signal Processing
## 1 Introduction
### Unique Comb Benefits  
Beside potential gains in terms of reduced hardware complexity and power consumption, there are also other, transmission- and signal quality-related gains to be had from the use of combs. The central difference of using a comb instead of separate lasers is that the comb lines are essentially phase-locked to each other, which is illustrated by the expression for the electric field of a comb [61]:  
\[E(t)=\sum_{n}E_{n}\text{exp}[-i2\pi f_{n}t+\phi(t)+2\pi nf_{r}\Delta T(t)]. \tag{1}\]  
Here, \(f_{n}=nf_{r}+f_{0}\) are the frequency comb lines, with fixed complex amplitude, \(E_{n}\). The random functions \(\phi(t)\) and \(\Delta T(t)\) represent the phase and timing jitter noise in the comb. If the timing jitter of the comb can be controlled (that is, it can be ignored for all practical purposes), the phase noise is correlated among the comb lines. Such a broadband phase coherence constitutes a key resource in many metrology applications of frequency combs [62], but this aspect has hitherto been ignored in most WDM systems where the channels are measured on an individual basis. Controlling the timing jitter is not always straightforward. However, the above equation also shows that the phase noise only depends on two random functions. This leads to the important property that the phase noise of all comb lines can be characterized by measuring the phase fluctuations of only two lines.  
In this paper, we will discuss how the stability in repetition rate and broadband phase coherence of frequency combs can be exploited in the design and operation of coherent WDM systems. The paper partly summarizes our work in [63; 64; 65; 66; 67; 68] and puts it into a broader context. Specifically, we focus on techniques for utilizing the phase coherence to relieve the digital carrier recovery in the receiver. In addition to reviewing previous work, we also present some previously unpublished results.  
The following unique features of optical frequency combs will be discussed:  
* They enable the WDM channels to be more densely packed, requiring smaller guard bands between the channels, since they drift in frequency in a correlated manner, in contrast to separate laser sources. Such comb-based superchannels will be discussed in Section 2.
* They enable optical pilot signals that can be co-transmitted with the data with unprecedented low overhead, since two pilots are sufficient to regenerate a local-oscillator comb phase-locked to the transmitter comb for 50 WDM channels or more. Such pilot-based comb regeneration will be discussed in Section 3.
* They enable joint digital signal processing with reduced complexity or increased phase-noise tolerance, since the retrieved phase from one channel can be reused for the other channels or used to increase the SNR of the phase estimate. Such joint signal processing algorithms will be discussed in Section 4.  
In addition, comb-based transmission enables other benefits that can be useful in WDM transmission, but will not be discussed in depth here. A notable example is the use of coherent combs for sub-band detection of high-bandwidth signals, for which electrical oscilloscopes cannot capture all features. Such metrology aspects have been explored by [PERSON] et al. [69]. This technique can also be utilized to measure wideband optical data signals [70]. Furthermore, in digital predistortion experiments to compensate for nonlinear WDM impairments, comb sources are needed to ensure frequency stability between channels [71; 72].  
This review is organized as follows: Section 2 is devoted to comb-based superchannels and their transmitter considerations, and Section 3 deals with the use of combs in receivers and regeneration of combs from optical pilots. Section 4 deals with joint receiver algorithms, i.e., sharing phase information between channels in DSP. Finally, in Section 4, we conclude this paper.