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Digital Channel Equalizer Using Functional Link Artificial Neural Network Trained with Quantum Aquila Optimizer

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Abstract

In digital communication, channel equalization plays an important role in mitigating the effects of inter-symbol interference, non-linearity and noise. In case of wireless channels, it also reduces the co-channel and adjacent channel interference. The channel equalizer is placed at the receiver which inherently perform an inverse modeling operation. In this manuscript, equalizers are proposed based on Functional Link Artificial Neural Network (FLANN) for nonlinear communication channel. Three types of FLANN architecture are explored based on: Trigonometric, Chebyshev and Legendre polynomial-based expansions. The weight of these FLANN architectures are trained by a quantum Aquila optimization algorithm (QAOA). In this manuscript the quantum entanglement principle is embodied to improve the performance of original Aquila optimizer. The Aquila optimizer is reported in 2021 by Abualigah et. al. is a popular algorithm and based on the inherent behavior of Aquila to catch the pray. Simulation studies are reported for two nonlinear finite impulse response (FIR) channels performance under noisy environment. The performance is reported in the form of MSE and normalized MSE (dB) value, run time required during training; final bit error rate (BER) value obtained and BER plot during testing. Simulation results reveal superior performance of Chebyshev FLANN architecture with QAOA learning, compared to the other FLANN models as well as a FIR filter-based equalizer trained with original Aquila optimizer, Grey Wolf optimizer, particle swarm optimizer and least mean square algorithm.

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Data Availability

The author declares that all the signals are generated using equations given in the manuscript. The parameters used in the equations are mentioned in the manuscript. There is no further associated data with this manuscript.

References

  1. Kollar I, Rolain Y. Complex correction of data acquisition channels using fir equalizer filters. IEEE Trans Instrum Meas. 1993;42(5):920–4.

    Article  ADS  Google Scholar 

  2. Larimore M, Treichler J, Johnson C. SHARF: an algorithm for adapting IIR digital filters. IEEE Trans Acoust Speech Signal Process. 1980;28(4):428–40.

    Article  Google Scholar 

  3. Song L, Tugnait JK. Doubly-selective fading channel equalization: a comparison of the Kalman filter approach with the basis expansion model-based equalizers. IEEE Trans Wirel Commun. 2009;8(1):60–5.

    Article  Google Scholar 

  4. Park S, Choi S. Iterative equalizer based on Kalman filtering and smoothing for MIMO-ISI channels. IEEE Trans Signal Process. 2015;63(19):5111–20.

    Article  ADS  MathSciNet  Google Scholar 

  5. Marcos S. A network of adaptive Kalman filters for data channel equalization. IEEE Trans Signal Process. 2000;48(9):2620–7.

    Article  ADS  MathSciNet  Google Scholar 

  6. Ling F, Proakis J. Adaptive lattice decision-feedback equalizers-their performance and application to time-variant multipath channels. IEEE Trans Commun. 1985;33(4):348–56.

    Article  Google Scholar 

  7. Ogunfunmi T, Drullinger T. In: 2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS). IEEE; 2011. p. 1–4.

  8. Malone J, Wickert MA. In: 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE). IEEE; 2011. p. 48–53.

  9. Nanda SJ, Jonwal N. Robust nonlinear channel equalization using WNN trained by symbiotic organism search algorithm. Appl Soft Comput. 2017;57:197–209.

    Article  Google Scholar 

  10. Zhang J, Lei P, Hu S, Zhu M, Yu Z, Xu B, Qiu K. Functional-link neural network for nonlinear equalizer in coherent optical fiber communications. IEEE Access. 2019;7:149900–7.

    Article  Google Scholar 

  11. Burse K, Yadav RN, Shrivastava S. Channel equalization using neural networks: a review. IEEE Trans Syst Man Cybern Part C (Appl Rev). 2010;40(3):352–7.

    Article  Google Scholar 

  12. Carrera DF, Vargas-Rosales C, Yungaicela-Naula NM, Azpilicueta L. Comparative study of artificial neural network based channel equalization methods for mmWave communications. IEEE Access. 2021;9:41678–87.

    Article  Google Scholar 

  13. Parisi R, Di Claudio ED, Orlandi G, Rao BD. Fast adaptive digital equalization by recurrent neural networks. IEEE Trans Signal Process. 1997;45(11):2731–9.

    Article  ADS  Google Scholar 

  14. Ahmad ST, Kumar KP. Radial basis function neural network nonlinear equalizer for 16-QAM coherent optical OFDM. IEEE Photonics Technol Lett. 2016;28(22):2507–10.

    Article  ADS  CAS  Google Scholar 

  15. Bansbach EM, von Bank A, Schmalen L. In: WSA & SCC 2023; 26th International ITG Workshop on Smart Antennas and 13th Conference on Systems, Communications, and Coding. VDE; 2023. p. 1–6.

  16. Huang W, Zhang L, Wu H, Min F, Song A. Channel-equalization-HAR: a light-weight convolutional neural network for wearable sensor based human activity recognition. IEEE Trans Mob. Comput. 2022;22(9):5064–77.

    Google Scholar 

  17. Caciularu A, Burshtein D. Unsupervised linear and nonlinear channel equalization and decoding using variational autoencoders. IEEE Trans Cognit Commun Netw. 2020;6(3):1003–18.

    Article  Google Scholar 

  18. Mohamed MA, Hassan HA, Essai MH, Esmaiel H, Mubarak AS, Omer OA. Modified gate activation functions of bi-LSTM-based SC-FDMA channel equalization. J Electr Eng. 2023;74(4):256–66.

    Google Scholar 

  19. Patra JC, Pal RN, Baliarsingh R, Panda G. Nonlinear channel equalization for QAM signal constellation using artificial neural networks. IEEE Trans Syst Man Cybern Part B (Cybern). 1999;29(2):262–71.

    Article  CAS  Google Scholar 

  20. Patra JC, Kot AC. Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans Syst Man Cybern Part B (Cybern). 2002;32(4):505–11.

    Article  CAS  Google Scholar 

  21. Patra JC, Poh WB, Chaudhari NS, Das A. In: Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005, vol. 5. IEEE; 2005. p. 3214–9.

  22. Patra JC, Chin WC, Meher PK, Chakraborty G. In: 2008 IEEE International Conference on Systems, Man and Cybernetics. IEEE; 2008. p. 1826–31.

  23. Patra JC, Meher PK, Chakraborty G. Nonlinear channel equalization for wireless communication systems using Legendre neural networks. Signal Process. 2009;89(11):2251–62.

    Article  Google Scholar 

  24. Nanda SJ, Garg S. Design of supervised and blind channel equalizer based on moth-flame optimization. J Inst Eng (India) Ser B. 2019;100:105–15.

    Article  Google Scholar 

  25. Das G, Pattnaik PK, Padhy SK. Artificial neural network trained by particle swarm optimization for non-linear channel equalization. Expert Syst Appl. 2014;41(7):3491–6.

    Article  Google Scholar 

  26. Mohapatra PK, Rout SK, Bisoy SK, 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.

    Article  ADS  Google Scholar 

  27. Mohapatra PK, Rout SK, Bisoy SK, Sain M. Training strategy of fuzzy-firefly based ANN in non-linear channel equalization. IEEE Access. 2022;10:51229–41.

    Article  Google Scholar 

  28. Shwetha N, Priyatham M, Gangadhar N. Artificial neural network based channel equalization using battle royale optimization algorithm with different initialization strategies. Multimed Tools Appl. 2024;83:15565–90.

    Article  Google Scholar 

  29. Ingle KK, Jatoth RK. An efficient Jaya algorithm with Lévy flight for non-linear channel equalization. Expert Syst Appl. 2020;145: 112970.

    Article  Google Scholar 

  30. Ingle KK, Jatoth RK. Non-linear channel equalization using modified grasshopper optimization algorithm. Appl Soft Comput. 2024;153:110091.

    Article  Google Scholar 

  31. Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-Qaness MA, Gandomi AH. Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng. 2021;157: 107250.

    Article  Google Scholar 

  32. Abualigah L. MatLab code of aquila optimizer: a novel meta-heuristic optimization algorithm. 2023. https://www.mathworks.com/matlabcentral/fileexchange/89381-aquila-optimizer-a-meta-heuristic-optimization-algorithm

  33. Zhao J, Gao ZM, Chen HF. The simplified aquila optimization algorithm. IEEE Access. 2022;10:22487–515.

    Article  Google Scholar 

  34. Yu H, Jia H, Zhou J, Hussien A. Enhanced aquila optimizer algorithm for global optimization and constrained engineering problems. Math Biosci Eng. 2022;19(12):14173–211.

    Article  PubMed  Google Scholar 

  35. Ekinci S, Izci D, Abualigah L. A novel balanced aquila optimizer using random learning and Nelder–Mead simplex search mechanisms for air-fuel ratio system control. J Braz Soc Mech Sci Eng. 2023;45(1):68.

    Article  CAS  Google Scholar 

  36. Baş E. Binary aquila optimizer for 0–1 knapsack problems. Eng Appl Artif Intell. 2023;118: 105592.

    Article  Google Scholar 

  37. Nadimi-Shahraki MH, Taghian S, Mirjalili S, Abualigah L. Binary aquila optimizer for selecting effective features from medical data: a Covid-19 case study. Mathematics. 2022;10(11):1929.

    Article  Google Scholar 

  38. Zeng L, Li M, Shi J, Wang S. Spiral aquila optimizer based on dynamic gaussian mutation: applications in global optimization and engineering. Neural Process Lett. 2023;55:11653–99.

    Article  Google Scholar 

  39. Jamazi C, Manita G, Chhabra A, Manita H, Korbaa O. Mutated Aquila optimizer for assisting brain tumor segmentation. Biomed Signal Process Control. 2024;88:105089.

    Article  Google Scholar 

  40. Verma M, Sreejeth M, Singh M, Babu TS, Alhelou HH. Chaotic mapping based advanced aquila optimizer with single stage evolutionary algorithm. IEEE Access. 2022;10:89153–69.

    Article  Google Scholar 

  41. Sharma A, Nanda SJ. Memory guided Aquila optimization algorithm with controlled search mechanism for seismicity analysis of earthquake prone regions. Appl Soft Comput. 2023:110894.

  42. Gul F, Mir I, Mir S. Aquila optimizer with parallel computing strategy for efficient environment exploration. J Ambient Intell Humaniz Comput. 2023;14(4):4175–90.

    Article  Google Scholar 

  43. Xing Q, Wang J, Lu H, Wang S. Research of a novel short-term wind forecasting system based on multi-objective Aquila optimizer for point and interval forecast. Energy Convers Manag. 2022;263: 115583.

    Article  Google Scholar 

  44. Nematollahi M, Ghaffari A, Mirzaei A. Task offloading in internet of things based on the improved multi-objective Aquila optimizer. Signal Image Video Process. 2024;18:545–52.

    Article  Google Scholar 

  45. Ait-Saadi A, Meraihi Y, Soukane A, Ramdane-Cherif A, Gabis AB. A novel hybrid chaotic aquila optimization algorithm with simulated annealing for unmanned aerial vehicles path planning. Comput Electr Eng. 2022;104: 108461.

    Article  Google Scholar 

  46. Mahajan S, Abualigah L, Pandit AK, Altalhi M. Hybrid aquila optimizer with arithmetic optimization algorithm for global optimization tasks. Soft Comput. 2022;26(10):4863–81.

    Article  Google Scholar 

  47. Abualigah L, Almotairi KH. Dynamic evolutionary data and text document clustering approach using improved aquila optimizer based arithmetic optimization algorithm and differential evolution. Neural Comput Appl. 2022;34(23):20939–71.

    Article  Google Scholar 

  48. Akyol S. A new hybrid method based on aquila optimizer and tangent search algorithm for global optimization. J Ambient Intell Humaniz Comput. 2023;14(6):8045–65.

    Article  PubMed  Google Scholar 

  49. Jnr EON, Ziggah YY, Rodrigues MJ, Relvas S. A hybrid chaotic-based discrete wavelet transform and aquila optimisation tuned-artificial neural network approach for wind speed prediction. Results Eng. 2022;14: 100399.

    Article  Google Scholar 

  50. Narasimhulu N, Krishnam Naidu R, Falkowski-Gilski P, Divakarachari PB, Roy U. Energy management for PV powered hybrid storage system in electric vehicles using artificial neural network and aquila optimizer algorithm. Energies. 2022;15(22):8540.

    Article  Google Scholar 

  51. AlRassas AM, Al-qaness MA, Ewees AA, Ren S, Abd Elaziz M, Damaševičius R, Krilavičius T. Optimized ANFIS model using Aquila optimizer for oil production forecasting. Processes. 2021;9(7):1194.

    Article  Google Scholar 

  52. Al-qaness MA, Ewees AA, Thanh HV, AlRassas AM, Abd Elaziz M. An optimized neuro-fuzzy system using advance nature-inspired Aquila and Salp swarm algorithms for smart predictive residual and solubility carbon trapping efficiency in underground storage formations. J Energy Storage. 2022;56: 106150.

    Article  Google Scholar 

  53. Nagapavithra S, Umamaheswari S. Detection and classification of sugarcane billet damage using aquila sailfish optimizer based deep learning. Artif Intell Rev. 2023;1–24.

  54. Hakemi S, Houshmand M, KheirKhah E, Hosseini SA. A review of recent advances in quantum-inspired metaheuristics. Evol Intell. 2022;1–16.

  55. Han KH, Kim JH. Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput. 2002;6(6):580–93.

    Article  Google Scholar 

  56. dos Santos Coelho L. Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl. 2010;37(2):1676–83.

    Article  Google Scholar 

  57. Li X, Fang W, Zhu S. An improved binary quantum-behaved particle swarm optimization algorithm for knapsack problems. Inf Sci. 2023;648: 119529.

    Article  Google Scholar 

  58. Liu M, Zhang F, Ma Y, Pota HR, Shen W. Evacuation path optimization based on quantum ant colony algorithm. Adv Eng Inform. 2016;30(3):259–67.

    Article  Google Scholar 

  59. Boushaki SI, Kamel N, Bendjeghaba O. A new quantum chaotic cuckoo search algorithm for data clustering. Expert Syst Appl. 2018;96:358–72.

    Article  Google Scholar 

  60. Vijay RK, Nanda SJ. A quantum Grey Wolf Optimizer based declustering model for analysis of earthquake catalogs in an ergodic framework. J Comput Sci. 2019;36: 101019.

    Article  Google Scholar 

  61. Rugema FX, Yan G, Mugemanyi S, Jia Q, Zhang S, Bananeza C. A Cauchy–Gaussian quantum-behaved bat algorithm applied to solve the economic load dispatch problem. IEEE Access. 2020;9:3207–28.

    Article  Google Scholar 

  62. Mirjalili S, Mirjalili SM, Lewis A. Grey Wolf Optimizer. Adv Eng Softw. 2014;69:46–61.

    Article  Google Scholar 

  63. Al-Awami AT, Zerguine A, Cheded L, Zidouri A, Saif W. A new modified particle swarm optimization algorithm for adaptive equalization. Digital Signal Process. 2011;21(2):195–207.

    Article  Google Scholar 

  64. Widrow B, Stearns SD. Adaptive signal processing. Pearson India; 2002.

  65. Nanda SJ, Panda G, Majhi B. In: 2008 IEEE Region 10 and the Third International Conference on Industrial and Information Systems. IEEE; 2008. 1–6.

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Correspondence to Arnapurna Panda.

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This article is part of the topical collection “Emerging Applications of Data Science for Real-World Problems” guest edited by Satyasai Jagannath Nanda, Rajendra Prasad Yadav and Mukesh Saraswat.

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Panda, A. Digital Channel Equalizer Using Functional Link Artificial Neural Network Trained with Quantum Aquila Optimizer. SN COMPUT. SCI. 5, 326 (2024). https://doi.org/10.1007/s42979-024-02632-8

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