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Performance of adaptive modulation with optimal switching thresholds for distributed antenna system in composite channels


In this paper, the performance of distributed antenna system (DAS) with adaptive modulation (AM) over a composite fading channel which takes path loss, Rayleigh fading, and log-normal shadowing into account is studied. Based on target bit error rate (BER), the AM scheme for DAS with average BER constraints is presented. The optimum switching thresholds (STs) for attaining maximum spectrum efficiency (SE) are derived by using Lagrange optimization method. An effective iterative algorithm based on Newton method for finding the optimal STs is proposed. With these thresholds, the closed-form expression of SE and average BER are derived for performance evaluation. Simulation results for SE and BER are in good agreement with the theoretical analysis. The results show that DAS-AM with optimal STs has higher SE than that with conventional fixed thresholds. Moreover, the proposed AM can fulfill the target BER for different signal-to-noise ratios (SNRs).

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  1. 1.

    Zhou S, Zhao M, Wang J, Yao Y (2003) Distributed wireless communication systems: a new architecture for future public wireless access. IEEE Commun Mag 41:108–113

    Article  Google Scholar 

  2. 2.

    Hu H, Zhang Y, Luo J (2007) Distributed antenna systems: open architecture for future wireless communications. Auerbach Publications, Germany

    Book  Google Scholar 

  3. 3.

    Choi W, Anderws JG (2007) Downlink performance and capacity of distributed antenna systems in a multicell environment. IEEE Trans Wireless Commun 6:69–73

    Article  Google Scholar 

  4. 4.

    Chen H-M, Chen M (2009) Capacity of the distributed antenna systems over shadowed fading channels. In: IEEE 69th vehicular technology conference spring (VTC’2009), pp 1–4

  5. 5.

    Wang J-Y, Wang J-B, Chen M (2011) System outage probability analysis of uplink distributed antenna systems over a composite channel. In: IEEE 73rd vehicular technology conference spring (VTC’2011), pp 1–5

  6. 6.

    Hu H, Weckerle M, Luo J (2006) Adaptive transmission mode selection scheme for distributed wireless communication systems. IEEE Commun Lett 10:573–575

    Google Scholar 

  7. 7.

    Chen H-M, Wang J-B, Chen M (2010) Spectral efficiency of the distributed MIMO system with antenna cooperation. In: IEEE 71st vehicular technology conference spring (VTC’2011), pp 1–4

  8. 8.

    Alouane WH, Hamdi N, Meherzi S (2014) Semi-blind amplify-and-forward in two-way relaying networks. Annal Telecommun 69:497–508

    Article  Google Scholar 

  9. 9.

    Alouini MS, Goldsmith AJ (2000) Adaptive modulation over Nakagami fading channel. Wireless Personal Commun 13:119–143

    Article  Google Scholar 

  10. 10.

    Zhou Z, Vucetic B, Dohler M, Li Y (2005) MIMO systems with adaptive modulation. IEEE Trans Vehicul Technol 54:1828–1842

    Article  Google Scholar 

  11. 11.

    Yu X, Rui Y, Yin X, Chen X, Li M (2012) Performance analysis of space-time coded MIMO system with discrete-rate adaptive modulation in Ricean fading channels. KSII Trans Int Informat Syst 6:2493–2508

    Google Scholar 

  12. 12.

    Yu X, Li Y, Zhou T, Xu D (2011) Performance of adaptive modulation with STBC and imperfect feedback information over Rayleigh fading channel. J Network 6:137–144

    Google Scholar 

  13. 13.

    Yu X, Leung S-H (2012) Performance analysis of rate-adaptive modulation with imperfect estimation in space-time coded MIMO system. Wireless Personal Commun 57:181–194

    Article  Google Scholar 

  14. 14.

    Chung ST, Goldsmith AJ (2001) Degrees of freedom in adaptive modulation: a unified view. IEEE Trans Commun 49:1561–1571

    MATH  Article  Google Scholar 

  15. 15.

    Choi B, Hanzo L (2003) Optimum mode-switching-assisted constant-power single-and multicarrier adaptive modulation. IEEE Trans Vehicul Technol 52:536–560

    Article  Google Scholar 

  16. 16.

    Youngwook K, Tepedelenlioglu C (2006) Orthogonal space-time block coded rate-adaptive modulation with outdated feedback. IEEE Trans Wireless Commun 5:290–295

    Article  Google Scholar 

  17. 17.

    Yu X, Tan W, Leung S-H, Rui Y, Liu X, Yin X (2013) Discrete-rate adaptive modulation with optimum switching thresholds for space-time coded multiple-input multiple-output system with imperfect channel state information. IET Commun 7:521–530

    MathSciNet  Article  Google Scholar 

  18. 18.

    Huang J, Signell S (2009) On performance of adaptive modulation in MIMO systems using orthogonal space-time block codes. IEEE Trans Vehicul Technol 58:4238–4247

    Article  Google Scholar 

  19. 19.

    Liu X, Yu X, Tan W, Tan W, Liu Y, Xu J (2013) Performance analysis of adaptive modulation in distributed MIMO systems. Int J Digit Cont Technol Appl 7:486–494

    Google Scholar 

  20. 20.

    Taylor BN (1995) Guide for the use of the international system of units (SI), Special Publication 811, US Department of Commerce, 1995 Edition, U.S

  21. 21.

    Cheikh DB, Kelif J-M, Coupechoux M, Godlewski P (2013) Multicellular Alamouti scheme performance in Rayleigh and shadow fading. Annals of Telecommunications 68:345–358

    Article  Google Scholar 

  22. 22.

    Stuber GL (1996) Principles of mobile communication. KIuwer Academic Publishers, Dordrecht, The Netherlands

  23. 23.

    Gradshteyn IS, Ryzhik IM (1994) Tables of integrals, series, and products. Academic, London

    Google Scholar 

  24. 24.

    Proakis JG (2007) Digital communications. McGraw-Hill, New York

    Google Scholar 

  25. 25.

    Cho K, Yoon D (2002) On the general BER expression of one- and two-dimensional amplitude modulations. IEEE Trans Wireless Commun 50:1074–1080

    Article  Google Scholar 

  26. 26.

    Hanzo L, Eebb WT, Keller T (2000) Single-and multi-carrier quadrature amplitude modulation. Wiley, New York

    Google Scholar 

  27. 27.

    Abramowitz M, Stegun IA (2012) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New York

    Google Scholar 

  28. 28.

    Shi Z, Leib H (2008) Transmit antenna selected V-BLAST systems with power allocation. IEEE Trans Vehicul Technol 57:2293–2304

    Article  Google Scholar 

Download references


The authors would like to thank the anonymous reviewers and Editor for their valuable comments and suggestions which improve the quality of this paper greatly. This work is partially supported by National Natural Science Foundation of China (61172077), Open Research Fund of National Mobile Communications Research Laboratory of Southeast University (2012D17), Innovation Fund of College of Electronic and Information Engineering of NUAA (DZS201201), PAPD of Jiangsu Higher Education Institutions, the Fundamental Research Funds for the Central Universities, Research Founding of Graduate Innovation Center in NUAA (kfjj201429), and Qing Lan Project of Jiangsu Province.

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Correspondence to Xiangbin Yu.



In this Appendix, we give the specific expression of Jacobi matrix DG(y (l)) in (29) by means of theoretical analysis and derivation. With (28), using the partial derivative operation, (29) can be rewritten as follows:

$$ DG\left({y}^{(l)}\right)=\left[\begin{array}{c}\hfill {\left[\nabla {G}_1\left({y}^{(l)}\right)\right]}^T\hfill \\ {}\hfill {\left[\nabla {G}_2\left({y}^{(l)}\right)\right]}^T\hfill \\ {}\hfill \vdots \hfill \\ {}\hfill {\left[\nabla {G}_U\left({y}^{(l)}\right)\right]}^T\hfill \\ {}\hfill {\left[\nabla {G}_{U+1}\left({y}^{(l)}\right)\right]}^T\hfill \end{array}\right]=\left[\begin{array}{ccccc}\hfill \partial {G}_1/\partial {\tilde{\gamma}}_1^{(l)}\hfill & \hfill 0\hfill & \hfill \cdots \hfill & \hfill 0\hfill & \hfill \partial {G}_1/\partial {\eta}^{(l)}\hfill \\ {}\hfill 0\hfill & \hfill \partial {G}_2/\partial {\tilde{\gamma}}_2^{(l)}\hfill & \hfill \cdots \hfill & \hfill 0\hfill & \hfill \partial {G}_2/\partial {\eta}^{(l)}\hfill \\ {}\hfill \vdots \hfill & \hfill \vdots \hfill & \hfill \ddots \hfill & \hfill \vdots \hfill & \hfill \vdots \hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill \cdots \hfill & \hfill \partial {G}_U/\partial {\tilde{\gamma}}_U^{(l)}\hfill & \hfill \partial {G}_U/\partial {\eta}^{(l)}\hfill \\ {}\hfill \partial {G}_{U+1}/\partial {\tilde{\gamma}}_1^{(l)}\hfill & \hfill \partial {G}_{U+1}/\partial {\tilde{\gamma}}_2^{(l)}\hfill & \hfill \cdots \hfill & \hfill \partial {G}_{U+1}/\partial {\tilde{\gamma}}_U^{(l)}\hfill & \hfill 0\hfill \end{array}\right] $$

Using (12) and (28), the nonzero elements of DG(y (l)) in (30) can be expressed as:

$$ \partial {G}_1/\partial {\tilde{\gamma}}_1^{(l)}=-{\eta}^{(l)}{b}_1{\alpha}_1\sqrt{\tau_1/\left(\pi {\tilde{\gamma}}_1^{(l)}\right) \exp \left(-{\tau}_1{\tilde{\gamma}}_1^{(l)}\right)} $$
$$ \partial {G}_1/\partial {\eta}^{(l)}={b}_1{\alpha}_1 erfc\left\{\sqrt{\tau_1{\tilde{\gamma}}_1^{(l)}}\right\}-{b}_1 BE{R}_0 $$
$$ \partial {G}_i/\partial {\tilde{\gamma}}_i^{(l)}={\eta}^{(l)}{\left(\pi {\tilde{\gamma}}_i^{(l)}\right)}^{-0.5}\left[{b}_{i-1}{\alpha}_{i-1}\sqrt{\tau_{i-1} \exp \left(-{\tau}_{i-1}{\tilde{\gamma}}_i^{(l)}\right)}-{b}_i{\alpha}_i\sqrt{\tau_i \exp \left(-{\tau}_i{\tilde{\gamma}}_i^{(l)}\right)}\right],\kern1em i=2,3,\dots, U. $$
$$ \partial {G}_i/\partial {\eta}^{(l)}=\left({b}_{i-1}-{b}_i\right) BE{R}_0+{b}_i{\alpha}_i erfc\left\{\sqrt{\tau_i{\gamma}_i^{(l)}}\right\}-{b}_{i-1}{\alpha}_{i-1} erfc\left\{\sqrt{\tau_{i-1}{\tilde{\gamma}}_i^{(l)}}\right\},\kern1em i=2,3,\dots, U. $$
$$ \partial {G}_{U+1}/\partial {\tilde{\gamma}}_1^{(l)}={b}_1\left[ BE{R}_0-{\alpha}_1 erfc\left\{\sqrt{\tau_1{\tilde{\gamma}}_1^{(l)}}\right\}\right]{f}_{\gamma}\left({\tilde{\gamma}}_1^{(l)}\right) $$
$$ \partial {G}_{U+1}/\partial {\tilde{\gamma}}_i^{(l)}=\left[\left({b}_i-{b}_{i-1}\right) BE{R}_0+{b}_{i-1}{\alpha}_{i-1} erfc\left\{\sqrt{\tau_{i-1}{\tilde{\gamma}}_i^{(l)}}\right\}-{b}_i{\alpha}_i erfc\left\{\sqrt{\tau_i{\tilde{\gamma}}_i^{(l)}}\right\}\right]{f}_{\gamma}\left({\tilde{\gamma}}_i^{(l)}\right),\kern1em i=2,3,\kern0.5em \dots, U. $$

The other elements are zero (as shown in (30)), where f γ (r) is the PDF of γ (see (11)). According to the derived expressions above, the corresponding elements will be nonzero. Based on this, using the elementary row transformation of matrix or calculating the determinant of matrix, we can conclude that (30) is a full-rank matrix. Thus, the matrix DF(x (l)) will be invertible.

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Wu, B., Yu, X., Wang, Y. et al. Performance of adaptive modulation with optimal switching thresholds for distributed antenna system in composite channels. Ann. Telecommun. 70, 415–426 (2015).

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  • Distributed antenna systems
  • Adaptive modulation
  • Thresholds optimization
  • Spectrum efficiency
  • Composite fading channel