# Application of Bat Algorithm and Its Modified Form Trained with ANN in Channel Equalization

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## Abstract

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## 1. Introduction

- Proposed a modified form of the bat algorithm trained with ANN in channel equalization.
- ANN-based nonlinear channel equalizers in wireless communication systems are trained using a modified version of the bat algorithm.
- Three nonlinear channels are tested to verify the superiority of the proposed work.
- Three nonlinearities were tested to prove how resilient the proposed scheme is, and the results revealed that the proposed work outperforms other methods in these situations.

## 2. Problem Description

## 3. Proposed Model

#### 3.1. Bat Algorithm

**BatDNN:**The BatDNN [43] is simplified as a basic dynamic neural network. Figure 1 shows the flow chart of the algorithm for optimizing the ANN model implemented. Generally, it consists of two parts of the solution for the population. In the ANN structure, the first part represents the ANN configuration, and the next part represents the W&B configurations. In the original population, the solution configurations are randomly distributed, W&B is determined to match every arrangement, and the significance of W&B is determined at the end randomly. The adjustments in frequency, velocity, and position are likely to be applied to the configuration solution. In both instances, the likelihood is the same. As is obvious from Figure 1 and the related calculations, the progress of every bat in the quest space is into constantly appreciated positions in this bat algorithm. The search space is established as a binary sample when the configuration result can be changed by the original frequency, velocity, and position [44]. We used the sigmoid attribute to represent the location of the bat in the binary vector.

**MBat-DNN [43]**: In a manner similar to that in the PSO standard [45], the basic bat algorithm keeps track of every bat’s location as ${f}_{i}$ monitors the pace as well as its movement. It uses loudness and pulse rate modulation as part of its integration of the PSO and local quest. The basic algorithm is similar to PSO, but we were motivated to continue our research by introducing the dominance of best in adjusting the PSO speed by personal best and global best. Bats are moved to the gbest in the standard bat algorithm, which causes the algorithm to experiment, while the influence of pbest is considered to increase the algorithm’s utilization in the updated form. We have altered the Equation (8) into Equation (13).

**Mean-BatDNN:**In the velocity update equation, as a substitute for comparing gbest and pbest, the present location of every bat is contrasted utilizing the linear amalgamation of the positions of pbest and gbest. As follows, we recommend a new velocity update equation:

#### 3.2. Modified Forms of Bat, Construction, and ANN Training

- Count the number of network errors in the training samples for each network.
- Examine all errors to determine the optimal problem space network.
- The network that has achieved the minimum error should be identified, the program should be terminated, and the weights should be recorded.
- Otherwise, each network’s position and velocity vector can be changed.
- Step 1 should be repeated again.

#### 3.3. The Training Procedure for the Proposed Algorithm with ANN

Algorithm 1. Training algorithm of the proposed equalizer. |

Assign ANN to a manager For j = 1, 2, … … L Create Bat -as supervisor (j)for ANN-as worker k = 1, 2, … … L make ANN- as worker end end While no solution has been established Update evaluation Specify the maximum number of iterations for ( Bat --as manager j = 1, 2, … … L)as (iterations<issuance) for (ANN-as worker k = 1, 2, … … M) test ANN-as worker (k) |

## 4. Simulations and Results

**Scenario: 1**

**Scenario: 2**

**Scenario: 3**

## 5. Conclusions

- Develop a learning procedure for ANNs.
- Make use of this algorithm trained with neural networks in channel equalization.
- In this work, the nonlinearities are used to evaluate the performance of different channels.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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SL. No. | Channel | Channel Type |
---|---|---|

CH0 | $H\left(Z\right)=0.260+0.930{Z}^{-1}+0.260{Z}^{-2}$ | MIXED |

CH1 | $H\left(Z\right)=0.303+0.9029{Z}^{-1}+0.3040{Z}^{-2}$ | MIXED |

CH2 | $H\left(Z\right)=1-0.90{Z}^{-1}+0.3850{Z}^{-2}+0.7710{Z}^{3}$ | MIXED |

SL. No. | Type of Nonlinearity |
---|---|

NL0 | ${y}_{2}\left(n\right)=\mathrm{tan}\mathrm{h}\left[s\left(n\right)\right]$ |

NL1 | ${y}_{2}\left(n\right)=s\left(n\right)+0.2{s}^{2}\left(n\right)-0.1{s}^{3}\left(n\right)$ |

NL2 | ${y}_{2}\left(n\right)=s\left(n\right)+0.2{s}^{2}\left(n\right)-0.1{s}^{3}\left(n\right)+0.5\mathrm{cos}\left[\pi s\left(n\right)\right]$ |

Size of Population | Algorithms | MSE | |||
---|---|---|---|---|---|

Best | Worst | Mean | Standard Deviation | ||

30 | PSO | 1.823 × 10^{−1} | 4.9023 × 10^{−1} | 2.4801 × 10^{−4} | 2.4221 × 10^{−4} |

BatDNN | 1.4319 × 10^{−5} | 1.2302 × 10^{−3} | 2.0821 × 10^{−5} | 4.6801 × 10^{−6} | |

MBat-DNN | 4.2318 × 10^{−5} | 1.3002 × 10^{−4} | 1.4821 × 10^{−6} | 8.4821 × 10^{−6} | |

Mean-BatDNN | 8.2371 × 10^{−6} | 5.0234 × 10^{−5} | 1.0721 × 10^{−7} | 6.2721 × 10^{−6} |

Size of Population | Algorithms | MSE | |||
---|---|---|---|---|---|

Best | Worst | Mean | Standard Deviation | ||

30 | PSO | 1.7233 × 10^{−5} | 3.8023 × 10^{−1} | 2.4821 × 10^{−1} | 6.3601 × 10^{−2} |

BatDNN | 1.0319 × 10^{−6} | 1.0302 × 10^{−3} | 3.0821 × 10^{−4} | 3.6801 × 10^{−4} | |

MBat-DNN | 4.1018 × 10^{−7} | 2.3002 × 10^{−4} | 2.4821 × 10^{−5} | 1.4821 × 10^{−4} | |

Mean-BatDNN | 1.2371 × 10^{−7} | 1.0234 × 10^{−5} | 2.0721 × 10^{−6} | 1.2721 × 10^{−4} |

Size of Population | Algorithms | MSE | |||
---|---|---|---|---|---|

Best | Worst | Mean | Standard Deviation | ||

30 | PSO | 17.4654 | 4.30 × 10 ^{2} | 1.0767 × 10 ^{1} | 67.0355 |

BatDNN | 3.2762 × 10^{−86} | 1.3764 × 10^{−70} | 3.6801 × 10^{−72} | 1.8767 × 10^{−71} | |

MBat-DNN | 2.2165 × 10^{−88} | 2.8906 × 10^{−72} | 8.4305 × 10^{−74} | 4.3087 × 10^{−73} | |

Mean-BatDNN | 5.5665 × 10^{−80} | 4.6863 × 10^{−47} | 9.7106 × 10^{−49} | 6.5042 × 10^{−48} |

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## Share and Cite

**MDPI and ACS Style**

Kumar Mohapatra, P.; Kumar Rout, S.; Kishoro Bisoy, S.; Kautish, S.; Hamzah, M.; Jasser, M.B.; Mohamed, A.W.
Application of Bat Algorithm and Its Modified Form Trained with ANN in Channel Equalization. *Symmetry* **2022**, *14*, 2078.
https://doi.org/10.3390/sym14102078

**AMA Style**

Kumar Mohapatra P, Kumar Rout S, Kishoro Bisoy S, Kautish S, Hamzah M, Jasser MB, Mohamed AW.
Application of Bat Algorithm and Its Modified Form Trained with ANN in Channel Equalization. *Symmetry*. 2022; 14(10):2078.
https://doi.org/10.3390/sym14102078

**Chicago/Turabian Style**

Kumar Mohapatra, Pradyumna, Saroja Kumar Rout, Sukant Kishoro Bisoy, Sandeep Kautish, Muzaffar Hamzah, Muhammed Basheer Jasser, and Ali Wagdy Mohamed.
2022. "Application of Bat Algorithm and Its Modified Form Trained with ANN in Channel Equalization" *Symmetry* 14, no. 10: 2078.
https://doi.org/10.3390/sym14102078