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Pilot pattern design scheme with branch and bound in PSA-OFDM system

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Abstract

Pilot symbol assisted (PSA) channel estimation is an important means to improve the communication quality of orthogonal frequency division multiplexing (OFDM) systems. The insertion position of the pilot in the frequency domain and time domain of the OFDM symbol is called the pilot pattern. The appropriate pilot pattern can greatly reduce channel estimation error and enhance communication quality. In this paper, the branch and bound (BnB) method is adopted to design the pilot pattern BnB-PP for the first time. Specifically, the result of the linear minimum mean square error method is taken as the target value of channel estimation in PSA-OFDM systems. For branching, pilot positions are randomly selected one by one in the form of the binary tree. For the boundary, after the pilots are filled randomly, a correction term is subtracted from the result of channel estimation at this time to present the expectation boundary. The results show that BnB-PP is better than the common pilot pattern. When signal-to-noise ratio is 36, the average MSE of channel estimation for 32 and 64 pilots in 1344 data signals is reduced by \(93.24\%\) and \(62.33\%\) respectively compared with the lattice-type pilot pattern.

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References

  • Acar Y, Aldırmaz-Çolak S (2021) A new spectrally efficient pilot scheme for OFDM systems. AEU-Int J Electron Commun 129:153566

    Article  Google Scholar 

  • Adegbite S, Stewart B, McMeekin S (2013) Least squares interpolation methods for LTE system channel estimation over extended ITU channels. Int J Inf Electron Eng 3(4):414

    Google Scholar 

  • Andrews JG, Buzzi S, Choi W, Hanly SV, Lozano A, Soong AC, Zhang JC (2014) What will 5g be? IEEE J Sel Areas Commun 32(6):1065–1082

    Article  Google Scholar 

  • Athaudage CR, Jayalath A (2003) Low-complexity channel estimation for wireless OFDM systems. In: 14th IEEE proceedings on personal, indoor and mobile radio communications, 2003. PIMRC 2003, vol 1, pp 521–525. IEEE

  • Athaudage CR, Jayalath ADS (2004) Enhanced MMSE channel estimation using timing error statistics for wireless OFDM systems. IEEE Trans Broadcast 50(4):369–376

    Article  Google Scholar 

  • Coleri S, Ergen M, Puri A, Bahai A (2002) Channel estimation techniques based on pilot arrangement in OFDM systems. IEEE Trans Broadcast 48(3):223–229

    Article  Google Scholar 

  • Colieri S, Ergen M, Puri A, Bahai A (2002) A study of channel estimation in OFDM systems. In: Proceedings IEEE 56th vehicular technology conference, vol 2, pp 894–898. IEEE

  • Edfors O, Sandell M, Van de Beek JJ, Wilson SK, Borjesson PO (1998) OFDM channel estimation by singular value decomposition. IEEE Trans Commun 46(7):931–939

    Article  Google Scholar 

  • Fu A, Modiano E, Tsitsiklis J (2003) Optimal energy allocation for delay-constrained data transmission over a time-varying channel. In: IEEE INFOCOM 2003. Twenty-second annual joint conference of the IEEE computer and communications societies (IEEE Cat. No. 03Ch37428), vol 2, pp 1095–1105. IEEE

  • He S, Zhang Q, Qin J (2021) Pilot pattern design for two-dimensional OFDM modulations in time-varying frequency-selective fading channels. IEEE Trans Wirel Commun

  • Hsieh MH, Wei CH (1998) Channel estimation for OFDM systems based on comb-type pilot arrangement in frequency selective fading channels. IEEE Trans Consum Electron 44(1):217–225

    Article  Google Scholar 

  • Kewen L, et al (2010) Research of MMSE and LS channel estimation in OFDM systems. In: The 2nd international conference on information science and engineering, pp 2308–2311. IEEE

  • Lin JC (2008) Least-squares channel estimation for mobile OFDM communication on time-varying frequency-selective fading channels. IEEE Trans Veh Technol 57(6):3538–3550

    Article  Google Scholar 

  • Liu Y, Tan Z, Hu H, Cimini LJ, Li GY (2014) Channel estimation for OFDM. IEEE Commun Surv Tutor 16(4):1891–1908

    Article  Google Scholar 

  • Ma J, Xue E, Dong X (2020) New pilot signal design on compressive sensing based random access for machine type communication. In: 2020 IEEE 8th international conference on information, communication and networks (ICICN). IEEE, pp 69–73

  • Mallach S (2018) Improved mixed-integer programming models for the multiprocessor scheduling problem with communication delays. J Comb Optim 36(3):871–895

    Article  MathSciNet  MATH  Google Scholar 

  • Mbugua AW, Chen Y, Raschkowski L, Thiele L, Jaeckel S, Fan W (2021) Review on ray tracing channel simulation accuracy in sub-6 GHz outdoor deployment scenarios. IEEE Open J Antennas Propag 2:22–37. https://doi.org/10.1109/OJAP.2020.3041953

    Article  Google Scholar 

  • Mi SS, Siriwanitpong A, Boonsrimuang P, Boonsrimuang P (2022) Channel estimation for enhanced subcarrier index modulation ofdm using zadoff-chu sequence pilot in nonlinear channel. In: 2022 19th international conference on electrical engineering/electronics. Computer, telecommunications and information technology (ECTI-CON). IEEE, pp 1–4

  • Morelli M, Mengali U (2001) A comparison of pilot-aided channel estimation methods for OFDM systems. IEEE Trans Signal Process 49(12):3065–3073

    Article  Google Scholar 

  • Morrison DR, Jacobson SH, Sauppe JJ, Sewell EC (2016) Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning. Discret Optim 19:79–102

    Article  MathSciNet  MATH  Google Scholar 

  • Muquet B, De Courville M, Duhamel P (2002) Subspace-based blind and semi-blind channel estimation for OFDM systems. IEEE Trans Signal Process 50(7):1699–1712

    Article  Google Scholar 

  • Panta KR, Armstrong J (2004) Effects of clipping on the error performance of OFDM in frequency selective fading channels. IEEE Trans Wirel Commun 3(2):668–671

    Article  Google Scholar 

  • Pratschner S, Tahir B, Marijanovic L, Mussbah M, Kirev K, Nissel R, Schwarz S, Rupp M (2018) Versatile mobile communications simulation: the Vienna 5G Link Level Simulator. EURASIP J Wirel Commun Netw 1:226. https://doi.org/10.1186/s13638-018-1239-6

    Article  Google Scholar 

  • Quadri D, Soutif E, Tolla P (2009) Exact solution method to solve large scale integer quadratic multidimensional knapsack problems. J Comb Optim 17(2):157–167

    Article  MathSciNet  MATH  Google Scholar 

  • Shi L, Guo B, Zhao L (2009) Block-type pilot channel estimation for OFDM systems under frequency selective fading channels

  • So J, Kim D, Lee Y, Sung Y (2014) Pilot signal design for massive MIMO systems: a received signal-to-noise-ratio-based approach. IEEE Signal Process Lett 22(5):549–553

    Article  Google Scholar 

  • Soltani M, Pourahmadi V, Mirzaei A, Sheikhzadeh H (2019) Deep learning-based channel estimation. IEEE Commun Lett 23(4):652–655

    Article  Google Scholar 

  • Soltani M, Pourahmadi V, Sheikhzadeh H (2020) Pilot pattern design for deep learning-based channel estimation in OFDM systems. IEEE Wirel Commun Lett 9(12):2173–2176

    Article  Google Scholar 

  • Soman AM, Nakkeeran R, Shinu MJ (2021) Pilot based MMSE channel estimation for spatial modulated OFDM systems. Int J Electron Telecommun 67(4):685–691

    Google Scholar 

  • Stuber GL, Barry JR, Mclaughlin SW, Li Y, Ingram MA, Pratt TG (2004) Broadband MIMO-OFDM wireless communications. Proc IEEE 92(2):271–294

    Article  Google Scholar 

  • Sun J, Yuan DF (2006) Neural network channel estimation based on least mean error algorithm in the OFDM systems. In: International symposium on neural networks. Springer, pp 706–711

  • Sutar MB, Patil VS (2017) LS and MMSE estimation with different fading channels for OFDM system. In: 2017 international conference of electronics, communication and aerospace technology (ICECA), vol 1, pp 740–745. https://doi.org/10.1109/ICECA.2017.8203641

  • Tian Y, Li K, Yang W, Li Z (2017) A new effective branch-and-bound algorithm to the high order MIMO detection problem. J Comb Optim 33(4):1395–1410

    Article  MathSciNet  MATH  Google Scholar 

  • Tong L, Sadler BM, Dong M (2004) Pilot-assisted wireless transmissions: general model, design criteria, and signal processing. IEEE Signal Process Mag 21(6):12–25

    Article  Google Scholar 

  • Tufvesson F, Maseng T (1997) Pilot assisted channel estimation for ofdm in mobile cellular systems. In: 1997 IEEE 47th vehicular technology conference, technology in motion, vol 3, pp 1639–1643. https://doi.org/10.1109/VETEC.1997.605836

  • Wang X (2005) OFDM and its application to 4g. In: 14th annual international conference on wireless and optical communications, 2005. WOCC 2005. IEEE, p 69

  • Wang CX, Huang J, Wang H, Gao X, You X, Hao Y (2020) 6g wireless channel measurements and models: trends and challenges. IEEE Veh Technol Mag 15(4):22–32. https://doi.org/10.1109/MVT.2020.3018436

    Article  Google Scholar 

  • Wu H (2021) LMMSE channel estimation in OFDM systems: a vector quantization approach. IEEE Commun Lett 25(6):1994–1998

    Article  Google Scholar 

  • Yu Q, Li R (2013) Research on pilot pattern design of channel estimation. J Autom Control Eng 1(2):160–163

    Article  Google Scholar 

  • Zhang W, Xia XG, Ching PC (2006) Optimal training and pilot pattern design for OFDM systems in Rayleigh fading. IEEE Trans Broadcast 52(4):505–514

    Article  Google Scholar 

  • Zhang L, Chen J, Udalcovs A, Louchet H, Dippon T, Gruen M, Pang X, Schatz R, Westergren U, Popov S et al (2019) Lattice pilot aided DMT transmission for optical interconnects achieving 5.820 bits/hz per lane

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Funding

This work was supported by the National Natural Science Foundation of China under Grant 11991022, 12071459.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Shuchen Wang, Suixiang Gao & Wenguo Yang

  2. Zhongguancun Laboratory, Beijing, China

    Suixiang Gao

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  1. Shuchen Wang
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  2. Suixiang Gao
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  3. Wenguo Yang
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Correspondence to Suixiang Gao.

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Wang, S., Gao, S. & Yang, W. Pilot pattern design scheme with branch and bound in PSA-OFDM system. J Comb Optim 45, 110 (2023). https://doi.org/10.1007/s10878-023-01037-2

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