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Power allocation and subchannel pairing for BER minimization in MIMO-OFDM AF relay systems

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Abstract

The present study investigates the problem of bit error rate minimization in multi-input-multi-output orthogonal frequency-division multiplexing amplify-and-forward relay systems. It is supposed that channels are frequency selective fading and under a total power constraint. In the multi-antenna transmitter, an independent symbol sequence is transmitted from each antenna. Zero forcing beamforming is performed in the reception and transmission of the relay to cancel out the inter-antenna interference. A power allocation and subchannel pairing scheme is considered as the optimization method. The goal of the optimization problem is to achieve the best bit error rate performance by applying a joint power allocation and subchannel pairing approach for all antennas. To deal with subchannel pairing, at first, we formulate it as a linear assignment problem and then Jonker-Volgenant algorithm is used to solve this problem. The joint scheme is compared with separate power allocation and subchannel pairing for each antenna as the main target. It is found that the joint scheme is superior to the separate method. Simulation results show that the proposed inter-antenna power allocation and subchannel pairing scheme can improve bit error rate and mean square error dramatically compared with separate subchannel pairing and power allocation at the cost of a little increase in complexity.

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References

  1. Gong S, Xing C, Ma S, Zhang Z, Fei Z (2019) Secure wideband beamforming design for two-way MIMO relaying systems. IEEE Trans Vehicular Technol 68(4)

  2. Singh AK, Mishra SK, Dixit S (2019) Energy efficiency in wireless sensor networks: cooperative MIMO-OFDM, Recent Trends in Communication, Computing, and Electronics. In: Lecture Notes in Electrical Engineering, vol 524. Springer, Singapore

    Google Scholar 

  3. Zhou G, Li Y, He Y-C, Wang X, Yu M (2018) Artificial fish swarm based power allocation algorithm for MIMO-OFDM relay underwater acoustic communication, IET Communications, Volume: 12. Issue 9

  4. Wireless LAN (2011) Medium Access Control (MAC) and Physical Layer (PHY) specifications Amendment 10: Mesh Networking. IEEE Standard 802.11 s

  5. Air interface for fixed and mobile broadband wireless access systems, IEEE Standerd 802.16j, 2006.

  6. Chia S, Gill T, Ibbetson L, Lister D, Pollard A, Irmer R, Almodovar D, Holmes N, Pike S (2008) 3G evolution. IEEE Microw. Mag. 9(4):52-63

    Article  Google Scholar 

  7. Loa K, Wu C, Sheu S, Yuan Y, Chion M, Huo D, Xu L (2010) IMT-advanced relay standards [WiMAX/LTE Update]. IEEE Commun. Mag. 48(8):40-48

    Article  Google Scholar 

  8. Chandrasekhar V, Andrews J, Gatherer A (2008) Femtocell networks: a survey. IEEE Commun. Mag. 46(9):59-67

    Article  Google Scholar 

  9. Wen M, Chen X, Li Q, Basar E, Wu Y-C, Zhang W (2019) Index modulation aided subcarrier mapping for dual-hop OFDM relaying. In: IEEE IEEE Transactions on Communications. 67(9):6012-6024

  10. Hammerstrom I, Wittneben A (2006) On the optimal power allocation for nonregenerative OFDM relay links. In: 2006 IEEE Int. Conf. Communications (ICC), pp 4463-4468

    Chapter  Google Scholar 

  11. Li Y, Wang W, Kong J, Hong W, Zhang X, Peng M (2008) Power allocation and subcarrier pairing in OFDM-based relaying networks. In: 2008 IEEE Int. Conf. Communications (ICC), pp 2602-2606

    Chapter  Google Scholar 

  12. Duval O, Hasan Z, Hossain E, Gagnon F, Bhargava VK (2010) Subcarrier selection and power allocation for amplify-and-forward relaying over OFDDM links. IEEE Trnas. Wireless Commun. 9(4):1293-1297

    Article  Google Scholar 

  13. Al-Tous H, Barhumi I (2014) A low complexity algorithm for selective AF-OFDM system. In: IEEE 79th Vehicular Technology Conf. (VTC Spring), pp 1-5

    Google Scholar 

  14. Xiong K, Fan P, Letaief KB, Yi S, Lei M (2012) Joint subcarrier-pairing and resource allocation for two-way multi-relay OFDM networks. In: 2012 IEEE Global Communications Conf. (GLOBECOM), pp 4874-4879

    Chapter  Google Scholar 

  15. Liu Y, Yan S, Li X, Shang Y (2014) Energy-efficient resource allocation for multi-user two-way relay-assisted OFDM system. In: 2014 21st Int. Conf. Telecommunications (ICT), pp 150-154

    Google Scholar 

  16. Mu H, Tao M, Dang W, Xiao Y (2009) Joint subcarrier-relay assignment and power allocation for decode-and-forward multi-relay OFDM systems. In: 4th Int. Conf. Communications Networking (ChinaCOM), China, pp 1-6

    Google Scholar 

  17. Liu Y, Tao M (2012) Optimal channel and relay assignment in OFDM based multi-relay multi-pair two-way communication networks. IEEE Trans. Commun. 60(2):317-321

    Article  Google Scholar 

  18. Biyanwilage S, Gunawardana U, Liyanapathirana R (2011) Selective subcarrier relaying and power allocation for multi-relay-assisted cooperative OFDM systems. In: 2011 Australian Communications Theory Workshop (AusCTW), pp 164-169

    Chapter  Google Scholar 

  19. Elgendy OA, Ismail MH, Elsayed K (2014) Max-min fair resource allocation for LTE-advanced relay-enhanced cells. In: 2014 IEEE Wireless Communications Networking Conf. (WCNC), pp 1432-1437

    Chapter  Google Scholar 

  20. Zhou Z, Zhu Q (2014) Joint optimization scheme for power allocation and subcarrier pairing in OFDM-based multi-relay networks. IEEE Commun. Lett 18(6):1039-1042

    Article  Google Scholar 

  21. Tao W, Glineur F, Louveaux J, Vandendorpe L (2013) Weighted sum rate maximization for downlink OFDMA With subcarrier-pair based opportunistic DF relaying. IEEE Trans. Signal Process. 61(10):2512-2524

    Article  MathSciNet  Google Scholar 

  22. Dang W, Tao M, Mu H, Huang J (2009) Subcarrier-pair based resource allocation for cooperative AF multi-relay OFDM systems. In: 2009 IEEE Global Communications Conf. (GLOBECOM), pp 1-6

    Google Scholar 

  23. Xu K, Zhang D, Xu Y, Ma W (2014) On the equivalence of two optimal power-allocation schemes for A-TWRC. IEEE Trans. Veh. Technol. 63(4):1970-1976

    Article  Google Scholar 

  24. Hammerstrom I, Wittneben A (2007) Power allocation schemes for amplify-and-forward MIMO-OFDM relay links, IEEE Trans. Wirel. Commun 6(8):2798-2802

    Google Scholar 

  25. Qin D, Wang Y, Zhou F (2017) SER optimization of OFDM based AF relaying in the presence of AWGGN. IEEE Access 5:3149-3156

    Article  Google Scholar 

  26. Qin D (2018) Rate optimization with proportional fairness for OFDM based relay systems. In: IEEE International Conference on Electronics Technology (ICET)

    Google Scholar 

  27. Gachhadar MNH, Qamar F, Siddiqui MHS, Noordin KA, Amiri IS (2018) Modified genetic algorithm based power allocation scheme for amplify-and-forward cooperative relay network. Comput Electr Eng

  28. Al-Tous H, Barhumi I (2014) Distributed resource allocation for multi-user multi-relay AF cooperative communication. In: 2014 8th International Conference on Signal Processing and Communication Systems (ICSPCS), pp 1-6

    Google Scholar 

  29. Qin D, Wang Y (2015) BER minimization for AF relay-assisted OFDM systems. IEEE Commun. Lett 19(3):495-498

    Article  MathSciNet  Google Scholar 

  30. Amin O, Uysal M (2011) Optimal bit and power loading for amplify-and forward cooperative OFDM systems. IEEE Trans Wireless Commun 10(3):772-781

    Article  Google Scholar 

  31. Boyd S, Vandenberghe L (2004) Convex Optimization. U.K. Cambridge Univ. Press, Cambridge

    Book  Google Scholar 

  32. Jonker R, Volgenant A (1987) A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38(4):325-340

    Article  MathSciNet  Google Scholar 

  33. 3rd Generation Partnership Project (2010) Technical specification group GSM/EDGE radio access network: radio transmission and reception, Cedex,France, TS 45.005 V8.8.0, Mar.2010.

  34. Amin O, Uysal M (2012) Adaptive power loading for multi-relay OFDM regenerative networks with relay selection. IEEE Trans Commun 60(3):614-619

    Article  Google Scholar 

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Correspondence to Yasser Attarizi.

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Appendix A

Appendix A

$$ {\left(\underset{n(x)}{\overset{m(x)}{\int }}h(t)\ \mathrm{dt}\right)}^{\prime }={m}^{\prime }(x).h\left(m(x)\right)-{n}^{\prime }(x).h\left(n(x)\right) $$
(A1)
$$ {\left(\sqrt{u}\right)}^{\prime }=\frac{u^{\prime }}{2\sqrt{u}} $$
(A2)
$$ Q(x)=\frac{1}{\sqrt{2\pi }}\ \underset{x}{\overset{\infty }{\int }}{e}^{-\frac{u^2}{2}}\kern0.5em \mathrm{du} $$
(A3)

The function of the optimization problem (36) can be expressed as follows:

$$ L=\sum \limits_{i=1}^{\mathrm{KN}}\sum \limits_{j=1}^{\mathrm{KN}}\frac{\rho_{i,j}u}{\sqrt{2\pi }}\underset{\left(\sqrt{v{\gamma}_{i,j}^{\mathrm{eq}}\frac{q_{i,j}}{\rho_{i,j}}}\right)}{\overset{\infty }{\int }}{e}^{-\frac{u^2}{2}}\kern1em \mathrm{du}\kern0.5em +\lambda \left(\sum \limits_{i=1}^{\mathrm{KN}}\sum \limits_{j=1}^{\mathrm{KN}}{q}_{i,j}-{P}_T\right) $$
(A4)

If it is applied, \( \frac{\partial L}{\partial {q}_{i,j}}=0 \):

$$ \left(0-\frac{\rho_{i,j}u}{2\sqrt{2\pi }}\kern0.5em \frac{v{\gamma}_{i,j}^{\mathrm{eq}}\frac{1}{\rho_{i,j}}}{\sqrt{v{\gamma}_{i,j}^{\mathrm{eq}}\frac{q_{i,j}}{\rho_{i,j}}}}\kern1.25em {e}^{-\frac{v{\gamma}_{i,j}^{\mathrm{eq}}\frac{q_{i,j}}{\rho_{i,j}}}{2}}\kern0.5em \right)+\lambda =0 $$
(A5)

The inverse function of f (x) = xex [34] and z = f−1(zez) = W(zez), where W(.) is the Lambert function. Thus, after some simple mathematical arrangements, it can be expressed as follows:

$$ \left(\ \frac{\rho_{i,j}u}{2\sqrt{2\pi }}\kern0.5em \frac{\sqrt{v{\gamma}_{i,j}^{\mathrm{eq}}\frac{1}{\rho_{i,j}}}}{\sqrt{q_{i,j}}}\kern1.25em {e}^{-\frac{v{\gamma}_{i,j}^{\mathrm{eq}}\frac{q_{i,j}}{\rho_{i,j}}}{2}}\kern0.5em \right)=\lambda $$
(A6)
$$ \left(\ {\left(\frac{\rho_{i,j}u}{2\sqrt{2\pi}\kern0.5em \lambda}\right)}^2\kern0.75em \frac{v{\gamma}_{i,j}^{\mathrm{eq}}}{\rho_{i,j}}\kern0.5em {e}^{-v{\gamma}_{i,j}^{\mathrm{eq}}\frac{q_{i,j}}{\rho_{i,j}}}\kern0.5em \right)={q}_{i,j} $$
(A7)

Next, multiplied the both sides at \( \left(\frac{v{\gamma}_{i,j}^{\mathrm{eq}}}{\rho_{i,j}}\right) \) as:

$$ {\left(\frac{\rho_{i,j}u}{2\sqrt{2\pi}\kern0.5em \lambda}\right)}^2\ {\left(\frac{v{\gamma}_{i,j}^{\mathrm{eq}}}{\rho_{i,j}}\right)}^2={q}_{i,j}\ {e}^{v{\gamma}_{i,j,}^{\mathrm{eq}}\frac{q_{i,j}}{\rho_{i,j}}}\ \left(\frac{v{\gamma}_{i,j}^{\mathrm{eq}}}{\rho_{i,j}}\right) $$
(A8)
(A9)

Finally, qi, j is given by:

$$ {q}_{i,j}=\left(\frac{\rho_{i,j}}{v{\gamma}_{i,j}^{eq}}\right)\ W\left[{\left(\frac{v{\gamma}_{i,j}^{eq}u}{2\sqrt{2\pi}\kern0.5em \lambda}\right)}^2\right] $$
(A10)

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Shamsesalehi, M., Attarizi, Y. & Rajabi, R. Power allocation and subchannel pairing for BER minimization in MIMO-OFDM AF relay systems. Ann. Telecommun. 75, 175–184 (2020). https://doi.org/10.1007/s12243-019-00737-3

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