Optimal Beamforming and Performance Analysis of Wireless Relay Networks with Unmanned Aerial Vehicle

Jian Ouyang; Min Lin

doi:10.1515/freq-2014-0065

Article

Optimal Beamforming and Performance Analysis of Wireless Relay Networks with Unmanned Aerial Vehicle

Jian Ouyang and Min Lin

Published/Copyright: January 28, 2015

Published by

Become an author with De Gruyter Brill

Author Information

From the journal Frequenz Volume 69 Issue 3-4

Abstract

In this paper, we investigate a wireless communication system employing a multi-antenna unmanned aerial vehicle (UAV) as the relay to improve the connectivity between the base station (BS) and the receive node (RN), where the BS–UAV link undergoes the correlated Rician fading while the UAV–RN link follows the correlated Rayleigh fading with large scale path loss. By assuming that the amplify-and-forward (AF) protocol is adopted at UAV, we first propose an optimal beamforming (BF) scheme to maximize the mutual information of the UAV-assisted dual-hop relay network, by calculating the BF weight vectors and the power allocation coefficient. Then, we derive the analytical expressions for the outage probability (OP) and the ergodic capacity (EC) of the relay network to evaluate the system performance conveniently. Finally, computer simulation results are provided to demonstrate the validity and efficiency of the proposed scheme as well as the performance analysis.

Keywords: unmanned aerial vehicle; wireless relay network; optimal beamforming; performance analysis

Appendix A

According to the definition of CDF, Fγtu can be obtained as

(A.1)Fγt(u)=Pr(γ1,tγ2,tγ1,t+γ2,t+1<u) =∫0uPr(γ2,t>u(γ1,t+1)γ1,t−u|γ1,t)fγ1,t(x)dx+∫u∞Pr(γ2,t<u(γ1,t+1)γ1,t−u|γ1,t)fγ1,t(x)dx =1−∫u∞[1−Fγ2,t((x+1)ux−u)]fγ1,t(x)dx

where fγ1,tx is the probability density function (PDF) of γ1,t and Fγ2,tx is the CDF of γ2,t. Here, g1,t experiences correlated Rician fading, the PDF expression of γ1,t=τtg1,tF2γˉ1 is expressed as [22]

(A.2)fγ1,t(x)=∑m=0∞∑n=0m(mn)(−1)nξmxN+n−1Γ(N+n)(2τtβγ¯1)N+nexp(−x2τtβγ¯1)(x≥0)

where β is the convergence parameter (1≤β≤4) and ξ0=1, ξm=∑n=0m−1δm−nξn/m for n≥1, with δm given in eq. (33). Meanwhile, since g2,t is subject to correlated Rayleigh fading, the PDF of γ2,t=1−τtg2,tF2γˉ2 has the formula [22]

(A.3)fγ2,t(x)= ∑i=1μ∑j=1viϑi,jxn−1Γ(j)((1−τt)λ2,t,iγ¯2)jexp(−x(1−τt)λ2,t,iγ¯2) (x≥0)

where ϑi,j is given in eq. (32). With the help of the identity [20, eq. 3.351.1]

∫0uxne−αxdx=n!αn+1−e−uα∑k=0nn!k!ukαn−k+1

, the CDF of γ2,t can be further calculated as

(A.4)Fγ2,t(x)=∫0xfγ2,t(y)dy=∑i=1μ∑j=1viϑi,jΓ(j)((1−τt)λ2,t,iγ¯2)j×∫0xyn−1exp(−y(1−τt)λ2,t,iγ¯2)dy =1−∑i=1μ∑j=1vi∑k=0j−1ϑi,jΓ(k+1)(x(1−τt)λ2,t,iγ¯2)k×exp(−x(1−τt)λ2,t,iγ¯2)

By using eqs (A.2) and (A.3) into (A.1), the CDF of γt can be written as

(A.5)Fγt(u)=1−∑i=1μ∑j=1vi∑k=0j−1∑m=0∞∑n=0m(mn)(−1)nϑi,jξmΓ(N+n)Γ(k+1)(12τtβγ¯1)N+n(1(1−τt)λ2,t,iγ¯2)k×∫u∞(u(x+1)x−u)kxN+n−1exp(−u(x+1)(x−u)(1−τ)λ2,t,iγ¯2−x2τtβγ¯1)dx︸I1

Following the change of variables as y=x−u, after some calculations, one can yield

(A.6)I1=exp(−(12τtβγ¯1+1(1−τ)λ2,t,iγ¯2)u)∑p=0k∑q=0N+n−1(kp)×(N+n−1q)uN+j+k−q−1(1+u)p×∫0∞yq−pexp(−u2+u(1−τ)λ2,t,iγ¯21y−y2τtβγ¯1)dy

Following the identity [20, eq. 3.471.9]

∫0∞xv−1exp(−βx−γx)dx=2(βγ)v2Kv(2βγ)

where Kv⋅ represents the vth order modified Bessel function of the second kind [20], after some mathematical computations, I1 can be computed as

(A.7)I1=2exp(−(12τtβγ¯1+1(1−τ)λ2,t,iγ¯2)u)∑p=0k∑q=0N+n−1(kp) ×(N+n−1q)(1(1−τ)λ2,t,iγ¯2)q−p+12 ×(12τtβγ¯1)p−q−12u2N+2N+2k−p−q−12 ×(1+u)p+q+12Kq−p+1(2u2+u2τt(1−τ)βγ¯1λ2,t,iγ¯2)

Finally, by substituting eq. (A.7) into eq. (A.5), we can obtain the CDF of γt as in eq. (30).

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 61271255), the Natural Science Foundation of Jiangsu Province (No. BK20131068 and BK20140883), the Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1402068B) and the Open Research Fund of National Mobile Communications Research Laboratory in Southeast University (No. 2012D15).

References

1. T.Samad, J. S.Bay, and D.Godbole, “Network-centric systems for military operations in urban terrain: the role of UAVs,” Proc. IEEE, vol. 95, pp. 92–107, Jan. 2007.10.1109/JPROC.2006.887327Search in Google Scholar

2. M.Berioli, A.Molinaro, S.Morosi, and S.Scalise, “Aerospace communications for emergency applications,” Proc. IEEE, vol. 99, pp. 1922–1938, Nov. 2011.Search in Google Scholar

3. E. W.Frew and T. X.Brown, “Airborne communication networks for small unmanned aircraft systems,” Proc. IEEE, vol. 96, pp. 2008–2027, Dec. 2008.Search in Google Scholar

4. Z.Han, A. L.Swindlehurst, and K. J. R.Liu, “Optimization of MANET connectivity via smart deployment/movement of unmanned air vehicles,” IEEE Trans. Veh. Technol., vol. 58, pp. 3533–3546, Sep. 2009.Search in Google Scholar

5. E. P.de Freitas, T.Heimfarth, I. F.Netto, et al.., “UAV relay network to support WSN connectivity,” in Proc. Int. Congress on UltraModern Telecommunications and Control Systems and Workshops, 2010.10.1109/ICUMT.2010.5676621Search in Google Scholar

6. O.Burdakov, P.Doherty, K.Holmberg, and P.-M.Olsson, “Optimal placement of UV-based communications relay nodes,” J. Global Optim., vol. 48, no. 4, pp. 511–531, Dec. 2010.10.1007/s10898-010-9526-8Search in Google Scholar

7. O.Burdakov, P.Doherty, K.Holmberg, J.Kvarnstrom, et al.., “Relay positioning for unmanned aerial vehicle surveillance,” Int. J. Rob. Res., vol. 29, no. 8, pp. 1069–1087, Jul. 2010.Search in Google Scholar

8. C.Dixon, and E. W.Frew, “Optimizing cascaded chains of unmanned aircraft acting as communication relays,” IEEE J. Sel. Areas Commun., vol. 30, pp. 883–898, Jun. 2012.10.1109/JSAC.2012.120605Search in Google Scholar

9. M. S.Sharawi, D. N.Aloi, and O. A.Rawashdeh, “Design and implementation of embedded printed antenna arrays in small UAV wing structures,” IEEE Trans. Antennas Propag., vol. 58, pp. 2531–2538, Aug. 2010.Search in Google Scholar

10. M.Lin, J.Ouyang, M.Li, L.Yang, et al., “BER analysis of MIMO transmit-receive beamforming schemes in rayleigh fading,” Frequenz, vol. 66, no. 1–2, pp. 33–39, Jan. 2012.10.1515/freq.2012.014Search in Google Scholar

11. P.Zhan, K.Yu, and A. L.Swindlehurst, “Wireless relay communications using an unmanned aerial vehicle,” in IEEE Workshop on Signal Processing Advances in Wireless Communications, 2006.10.1109/SPAWC.2006.346492Search in Google Scholar

12. P.Zhan, K.Yu, and A. L.Swindlehurst, “Wireless relay communications with unmanned aerial vehicles: Performance and optimization,” IEEE Trans. Aerosp. Electron. Syst., vol. 47, pp. 2068–2085, Jul. 2011.Search in Google Scholar

13. F.Jiang, and A. L.Swindlehurst, “Optimization of UAV heading for the ground-to-air uplink,” IEEE J. Sel Areas Commun., vol. 30, pp. 993–1005, Jun. 2012.10.1109/JSAC.2012.120614Search in Google Scholar

14. M.Li, M.Lin, Q.Yu, W. P.Zhu, et al., “Optimal beamformer design for dual-hop MIMO AF relay networks over Rayleigh fading channels,” IEEE J. Selected Areas Communications, vol. 30, pp. 1402–1414, Sep. 2012.Search in Google Scholar

15. J.Ouyang, M.Lin, and F.Yu, “Performance analysis of cooperative fixed-gain relaying over asymmetric fading channels,” Frequenz, vol. 68, no. 3–4, pp. 89–96, Mar. 2014.10.1515/freq-2013-0090Search in Google Scholar

16. R. H. Y.Louie, Y.Li, H. A.Suraweera, and B.Vucetic, “Performance analysis of beamforming in two hop amplify and forward relay networks with antenna correlation,” IEEE Trans. Wirel. Commun., vol. 8, pp. 3132–3141, Jun. 2009.Search in Google Scholar

17. T. S.Rappaport, Wireless Communications: Principles and Practice, 2nd ed. New Jersey, USA: Prentice Hall, 1996.Search in Google Scholar

18. G. H.Golub, and C. F.VanLoan. Matrix Computation, 3rd ed. Maryland, USA: Johns Hopkins University Press, 1996.Search in Google Scholar

19. D. B.da Costa, and S.Aissa, “Capacity analysis of cooperative systems with relay selection in Nakagami-m fading,” IEEE Commun. Lett., vol. 13, pp. 637–639, Sep. 2009.10.1109/LCOMM.2009.091136Search in Google Scholar

20. I. S.Gradshteyn, and I. M.Ryzhik, Table of Integrals, Series, and Products, 7th ed. Burlington, USA: Academic Press, 2007.Search in Google Scholar

21. R. R.Pitre, X. R.Li, and R.Delbalzo, “UAV route planning for joint search and track missions-an information-value approach,” IEEE Trans. Aerosp. Electron. Syst., vol. 48, pp.2551–2565, Jul. 2012.Search in Google Scholar

22. L.Musavian, M.Dohler, M. R.Nakhai, and A. H.Aghvami, “Closed-form capacity expressions of orthogonalized correlated MIMO channels,” IEEE Commun. Lett., vol. 8, pp. 365–367, Jun. 2004.10.1109/LCOMM.2004.827430Search in Google Scholar

Published Online: 2015-1-28

Published in Print: 2015-3-31

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/freq-2014-0065

Keywords for this article

unmanned aerial vehicle; wireless relay network; optimal beamforming; performance analysis