# Crosstalk Classification Based on Synthetically Consider Crosstalk and Fragmentation RMCSA in Multi-Core Fiber-Based EONs

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. System Model and the Enabling Technologies

#### 3.1. Network Model

^{i}) is modeled as R

^{i}(s

^{i}, d

^{i}, b

^{i}, ${t}_{s}^{i}$, ${t}_{e}^{i}$), which means the connection request from the source node s

^{i}to the destination node d

^{i}starts at ${t}_{s}^{i}$, ends at ${t}_{e}^{i}$ and requires b

^{i}(Gbps) bandwidth.

^{i}reaches the network dynamically, the number of FSs R

^{i}needed is first calculated. The number of FSs is then used to determine whether R

^{i}is established or blocked by the lightpath (P

^{i}) from node s

^{i}to d

^{i}. The number of FSs required by R

^{i}is determined by the size of the bandwidth demand and the selected modulation level, which can be calculated by Equation (1) [29]

^{i}and b

^{i}represent the number of FSs and bandwidth required by R

^{i}. M denotes modulation level (i.e., 1, 2, 3, 4). C

_{slot}is the bandwidth granularity of each FS. GB is the number of FS of the guard band required to ensure non-overlapping constraint. The FSs assigned to R

^{i}is expressed as [${f}_{s}^{i}$, ${f}_{e}^{i}$], where ${f}_{s}^{i}$ and ${f}_{e}^{i}$ are the indexes of start FS and end FS for R

_{i}, respectively.

#### 3.2. Three Domains XT-Fragmentation Metric Model

#### 3.2.1. Spatial Domain

_{i}

_{,j}and L represent the power coupling coefficient and the fiber length, respectively. h

_{i}

_{,j}is related to multiple parameters in MCF, which is mathematically expressed as Equation (3):

_{i,j}and k

_{i,j}are the core pitch and the mode coupling coefficient between cores i and j, respectively. According to optical waveguide theory, k

_{i}

_{,j}is calculated by Equation (4):

#### 3.2.2. Frequency Domain

_{1,2}since the two lightpaths in these cores have two FSs in common. Similarly, the overall inter-core XT suffered by a specific core may be expressed as Equation (6):

_{1,2}+ 4 ∙ XT

_{2,3}. because for core 2, 2 FSs are affected by XT with core 1 and 2 FSs with core 3.

_{2}.

#### 3.2.3. Time Domain

^{i}, both the ${t}_{s}^{i}$ and ${t}_{e}^{i}$ are considered, because the XT and fragmentation are only generated when the request occupies the resources in the network. Therefore, the time domain is also considered when computing the XT and fragmentation issues. In general, a longer lightpath request duration leads to more serious inter-core XT. Considering the time domain, we can further define the time-weighted inter-core XT as Equation (8):

#### 3.3. Routing and Modulation Format Selection

## 4. Crosstalk Classification Based on Synthetically Consider Crosstalk and Fragmentation Algorithm

#### 4.1. Crosstalk Classification Algorithm

^{i}(s

^{i}, d

^{i}, b

^{i}, ${t}_{s}^{i}$, ${t}_{e}^{i}$) arrives, we first judge whether there is any lightpath to be released in the connection R

^{el}. If so, we update R

^{el}and release the occupied spectrum resources (steps 1–5). Then, according to the KSP algorithm, the k-shortest paths are selected for R

^{i}and stored in the P

^{i}(steps 6). Next, the available modulation level (${M}_{j}^{i}$) is selected for each path in P

^{i}, where the highest modulation level (${M}_{max}^{i}$) is determined by transmission distance. For each ${M}_{j}^{i}$, the number of R

^{i}-occupied FSs (F

^{i}) is calculated according to Equation (1) (steps 7–12). By combining P

^{i}and ${M}_{j}^{i}$, the collaboration path (CP

^{i}) is obtained and is numbered in ascending order of F

^{i}(step 13). After that, we set the XT stage in CP

^{i}as CS

^{i}(steps 14–15). Next, we determine whether the core (c) in CP

^{i}contains appropriate idle spectrum blocks (SBs) under the CS

^{i}and store the SBs as B

^{i}(steps 16–18). Then, Algorithm 2 is used to determine whether B

^{i}meets the crosstalk constraint. If B

^{i}meets the crosstalk constraint, B

^{i}is stored as an alternative spectrum block (AB

^{i}) (steps 19–28), and AB

^{i}with the minimum degree (d

^{i}) of XT effect is allocated for R

^{i}(steps 29–30). Otherwise, R

^{i}will be blocked after the total paths are searched (steps 31–34).

Algorithm 1: CC algorithm | |

Input: Arriving connection request R^{i}(s^{i}, d ^{i}, b^{i}, ${t}_{s}^{i}$, ${t}_{e}^{i}$). | |

Output: Spectrum allocation. | |

1: | for each existing connection R^{el}(s^{el}, d^{el}, b^{el}, ${t}_{s}^{el}$, ${t}_{e}^{el}$) do |

2: | if ${t}_{s}^{el}$ < ${t}_{e}^{el}$ then |

3: | Update R^{el} and release the occupied spectrum resources. |

4: | end if |

5: |
end for |

6: | Select the k-shortest paths for R^{i} according to the KSP algorithm and store in the P^{i} |

7: | for each P^{i} do |

8: | Determine the highest modulation format level ${M}_{max}^{i}$. |

9: | for each modulation level ${M}_{j}^{i}$ in [${M}_{1}^{i}$, ${M}_{max}^{i}$] do |

10: | Compute the number of FSs F_{i} requested by Equation (1). |

11: | end for |

12: | end for |

13: | CP^{i} is numbered in ascending order of F^{i} |

14: | for each collaboration path CP^{i} do |

15: | Set the XT stage as CS^{i}_{.} |

16: | for each CS^{i} do |

17: | for each c of CP^{i} do |

18: | According to the size of SBs and the crosstalk threshold, search the available SBs as B^{i}. |

19: | if B^{i} ≠ None then |

20: | for each B^{i} do |

21: | Compute XT based on Algorithm 2. |

22: | if Algorithm 2 returns 1 then |

23: | Store the B^{i} in AB^{i} |

24: | Break. |

25: | end if |

26: | end for |

27: | end if |

28: | end for |

29: | if AB^{i} ≠ None then |

30: | Select the SB with the first minimum of d^{i} and allocate the d^{i} for R^{i}. |

31: | end if |

32: | Reject connection request R^{i} |

33: | end for |

34: |
end for |

#### 4.2. Synthetically Consider Crosstalk and Fragmentation Algorithm

_{i,j}denotes the number of FSs in which affected by XT.

Algorithm 2: SCCF algorithm | |

Input: P^{i}, c^{i}, ${f}_{s}^{i}$, ${f}_{e}^{i}$. | |

Output: 1 or 0. | |

1: | XT = 0. |

2: | for FS f^{i} in [${f}_{s}^{i}$, ${f}_{e}^{i}$] do |

3: | for (link e^{i}, core c^{i}) in P^{i} do |

4: | for each adjacent ${c}_{a}^{i}$ of c^{i} do |

5: | if R^{el} ≠ None then |

6: | for each e^{el} do |

7: | Calculate ${XT}_{i,j}^{F,\mathrm{T}}$, ${XT}_{i}^{F,\mathrm{T}}$, and ${CI}_{i}^{F,\mathrm{T}}$. |

8: | end for |

9: | if ${XT}_{i}^{F,\mathrm{T}}$ > XT_{threshold} then |

10: | return 0 |

11: | end if |

12: | end if |

13: | end for |

14: |
end for |

15: | Select the spectrum resource with minimal ${CI}_{i}^{F,\mathrm{T}}$ |

16: | if ${XT}_{i,j}^{F,\mathrm{T}}$ > XT_{threshold} then |

17: | return 0 |

18: | end if |

19: |
end for |

20: | return 1 |

^{i}on the path, core c

^{i}, the start FS ${f}_{s}^{i}$, and the end FS ${f}_{e}^{i}$. The output of the algorithm is a Boolean number: 1 indicates that the new lightpath can be successfully transmitted over these pre-allocated FS, and 0 indicates that the lightpath cannot be transmitted.

^{i}, and c

^{i}(steps 1–4). Then, we determine the occupation status of adjacent cores at the f

^{i}of R

^{el}transmission (steps 5–7). If the spectrum resources are being occupied by lightpaths, we calculate the XT ${XT}_{i,j}^{F,\mathrm{T}}$ by Equation (16) and check if it meets the XT

_{threshold}to ensure transmission successfully (steps 8–14). Finally, we compute and judge whether the XT on each FS assigned for P

^{i}is less than the XT

_{threshold}, and select the SB with the lowest total crosstalk effect (steps 15–20).

_{i}itself is calculated and checked to determine if it is less than XT

_{threshold}and choose the spectrum resources with minimal combined impact (steps 15–20).

#### 4.3. Complexity

^{2}|E|

^{2}|M||N||S|

^{2}log|V|).

## 5. Simulation Results and Analysis

#### 5.1. Performance Comparison of Blocking Probability

#### 5.2. Network-Wide XT Effect Ratio

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Comparison of Combined Impact Ratio for different weights (α) in (

**a**) COST239 and (

**b**) NSFNET.

**Table 1.**The parameters are used to determine the transmission reach, capacity per frequency slot, and XT thresholds for each modulation format.

Modulation Formats | Transmission Reach [km] | Capacity pFS [GHz] | XT Thresholds [dB] |
---|---|---|---|

BPSK | 4000 | 12.5 | −14 |

QPSK | 2000 | 25 | −18.5 |

8-QAM | 1000 | 37.5 | −21 |

16-QAM | 500 | 50 | −25 |

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## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Feng, N.; Zhou, Y.; Ren, D.; Zhao, J.
Crosstalk Classification Based on Synthetically Consider Crosstalk and Fragmentation RMCSA in Multi-Core Fiber-Based EONs. *Photonics* **2023**, *10*, 340.
https://doi.org/10.3390/photonics10030340

**AMA Style**

Chen Y, Feng N, Zhou Y, Ren D, Zhao J.
Crosstalk Classification Based on Synthetically Consider Crosstalk and Fragmentation RMCSA in Multi-Core Fiber-Based EONs. *Photonics*. 2023; 10(3):340.
https://doi.org/10.3390/photonics10030340

**Chicago/Turabian Style**

Chen, Yanbo, Nan Feng, Yue Zhou, Danping Ren, and Jijun Zhao.
2023. "Crosstalk Classification Based on Synthetically Consider Crosstalk and Fragmentation RMCSA in Multi-Core Fiber-Based EONs" *Photonics* 10, no. 3: 340.
https://doi.org/10.3390/photonics10030340