Eq. (B.2.2) particularizing for GG atmospheric turbulence channels with zero boresight pointing errors and n = 1 as follows
E[Im] = A0mLmϕ2m
1 + ϕ2m . (B.3.3)
The expectation of IT is given by
E[IT] = A0SDLSDϕ2SD
1 + ϕ2SD + 2A0RDLRDϕ2RD
1 + ϕ2RD . (B.3.4)
Secondly, we obtain the expectation of positive square root of ITLB as
E
q ITLB
= Z ∞
0
i1/2fILB
T (i)di. (B.3.5)
The above integral can be evaluated as in Eq. (B.2.2) particularizing for GG atmospheric turbulence channels with zero boresight pointing errors and n = 1/2 as follows
E
q ITLB
= s
A0SDA0RDLSDLRD
αSDβSDαRDβRD
×4ϕ2SDΓ(αSD+ 1/2)Γ(βSD+ 1/2)ϕ2RDΓ(αRD+ 1/2)Γ(βRD+ 1/2) (1 + 2ϕ2SD)Γ(αSD)Γ(βSD)(1 + 2ϕ2RD)Γ(αRD)Γ(βRD) .
(B.3.6)
Finally, the correcting factor F is easily derived from Eqs. (B.3.4) and (B.3.6) as follows
F =
A0SDLSDϕ2SD
1 + ϕ2SD +2A0RDLRDϕ2RD 1 + ϕ2RD
2
× αSDβSD(1 + 2ϕ2SD)2Γ(αSD)2Γ(βSD)2 128A0SDLSDϕ4SDΓ(αSD+ 1/2)2Γ(βSD+ 1/2)2
× αRDβRD(1 + 2ϕ2RD)2Γ(αRD)2Γ(βRD)2 A0RDLRDϕ4RDΓ(αRD+ 1/2)2Γ(βRD+ 1/2)2.
(B.3.7)
B.4 Correcting Factor for the ADF Cooperative Protocol
The correcting factor F0 for the ADF coopertive protocol is obtained for GG atmospheric turbulence with zero boresight pointing errors under the assumption that IRD> ISD. In this way, we can express this correcting factor as follows
F0= E[ISD+ 2IRD]2 8· E√
ISDIRD
2, IRD> ISD. (B.4.1)
Similar to the correcting factor obtained in AppendixB.3, we firstly obtain the expectation
In order to evaluate the double integral in A, we have to evaluate the inner one first. In this way, we can obtain the corresponding closed-form expression of A with the help of [59, eqn.
1.16.2.1] and [59, eqn. 2.24.1.2] (See Appendix A.3.2) for the inner integral and the outer integral, respectively. Hence, the integral A can be expressed in terms of the Meijer’s G-function as follows Similar to A, we can obtain the corresponding closed-form expression of the integral B with the help of [59, eqn. 2.24.1.2] as
B = Secondly, we obtain the expectation of positive square root of the product of ISDIRD under the assumption that IRD > ISD as follows
E[
Similar to A, we can obtain the expectation of positive square root of the product of ISD and IRD as Finally, the correcting factor F0 is easily derived from Eqs. (B.4.3), (B.4.4) and (B.4.6) as follows
F0 = (A + 2B)2
8· C2 . (B.4.7)
Appendix C
Correlated Sways
In this Appendix, the corresponding means and variances of x0 and y0 are derived. In this way, the corresponding mean of x0 can easily be obtained as follows
µ0x= E[x0] = E[r cos(φ− φ0)] = E[r cos φ cos φ0+ r sin φ sin φ0]
= cos φ0E[r cos φ] + sin φ0E[r sin φ] = µxcos φ0+ µysin φ0. (C.0.1) Similar to the above expression, the corresponding mean of y0 is also obtained as follows
µ0y = E[y0] = E[r sin(φ− φ0)] = E[r sin φ cos φ0− r cos φ sin φ0]
= cos φ0E[r sin φ]− sin φ0E[r cos φ] = µycos φ0− µxsin φ0. (C.0.2) Finally, the corresponding variance of x0 can be obtained by performing some easy algebraic manipulations as follows
σ0x2 = V ar[x0] = V ar[r cos(φ− φ0)] = V ar[r cos φ cos φ0+ r sin φ sin φ0]
= cos2φ0V ar[r cos φ] + sin2φ0V ar[r sin φ]
+ 2 cos φ0sin φ0Cov[r cos φ, r sin φ]
= σx2cos2φ0+ σ2ysin2φ0+ 2ρσxσysin φ0cos φ0.
(C.0.3)
Similar to the above expression, the corresponding variance of y0 is also obtained as follows σy02 = V ar[y0] = V ar[r sin(φ− φ0)] = V ar[r sin φ cos φ0− r cos φ sin φ0]
= cos2φ0V ar[r sin φ] + sin2φ0V ar[r cos φ]
− 2 cos φ0sin φ0Cov[r sin φ, r cos φ]
= σy2cos2φ0+ σ2xsin2φ0− 2ρσxσysin φ0cos φ0.
(C.0.4)
131
Appendix D
Publications and Projects
D.1 Publications
In this section, the publications derived during the development of this thesis are presented.
Book chapter
• R. Boluda-Ruiz, B. Castillo-V´azquez, C. Castillo-V´azquez, and A. Garc´ıa- Zambrana,
“New Results in DF Relaying Schemes Using Time Diversity for Free-Space Optical Links,” Dr. Narottam Das (Ed.), Chapter 8. InTech. pp.195-213, 2014. ISBN 978-953-51-1730-8.
Journal papers
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
”On the effect of correlated sways on generalized misalignment fading for terrestrial FSO links,” Photonics Journal, IEEE, 9(3), 1–13, 2017 (Impact factor 2.177, 60/257 Engineering, Electrical and Electronic Q1 JCR 2015).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, C. Castillo-V´azquez, B. Castillo-V´azquez, and Steve Hranilovic, ”Outage Performance of Exponentiated Weibull FSO Links Under Generalized Pointing Errors,” J. of Lightwave Technol., IEEE/OSA, vol. 35, no. 9, pp.
1605–1613, 2017 (Impact factor 2.567, 20/90 Optics Q1 JCR 2015).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, C. Castillo-V´azquez, and B. Castillo-V´azquez,
”Novel approximation of misalignment fading modeled by Beckmann distribution on free-space optical links,” Opt. Express 24(20), 22635–22649, 2016 (Impact factor 3.148, 14/90 Optics Q1 JCR 2015).
133
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
”Impact of nonzero boresight pointing error on ergodic capacity of MIMO FSO com-munication systems,” Opt. Express 24(4), 3513–3534, 2016 (Impact factor 3.148, 14/90 Optics Q1 JCR 2015).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
“Ergodic capacity analysis of decode-and-forward relay-assisted FSO systems over alpha-mu fading channels considering pointing errors,” Photonics Journal, IEEE, 8(1), 1–11, 2016 (Impact factor 2.177, 60/257 Engineering, Electrical and Electronic Q1 JCR 2015).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
“MISO relay-assisted FSO systems over gamma-gamma fading channels with pointing errors,” Photonics Technology Letters, IEEE 28(3), 229–232, 2016 (Impact factor 1.945, 72/257 Engineering, Electrical and Electronic Q2 JCR 2015).
• A. Garc´ıa-Zambrana, R. Boluda-Ruiz, C. Castillo-V´azquez, and B. Castillo-V´azquez,
“Novel space-time trellis codes for free-space optical communications using transmit laser selection,” Opt. Express 23(19), 24195–24211, 2015 (Impact factor 3.488, 9/86 Optics Q1 JCR 2013).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
“On the capacity of MISO FSO systems over gamma-gamma and misalignment fading channels,” Opt. Express 23(17), 22371–22385, 2015 (Impact factor 3.488, 9/86 Optics Q1 JCR 2013).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
“Ergodic capacity analysis for DF strategies in cooperative FSO systems,” Opt. Ex-press 23(17), 21565–21584, 2015 (Impact factor 3.488, 9/86 Optics Q1 JCR 2013).
• C. Castillo-V´azquez, R. Boluda-Ruiz, B. del Castillo-V´azquez, and A. Garc´ıa-Zambrana, “Outage performance of DF relay assisted FSO communications using time-diversity,” Photonics Technology Letters, IEEE 27(11), 1149–1152, 2015 (Im-pact factor 2.110, 56/249 Engineering, Electrical and Electronic Q1 JCR 2013).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, B. Castillo-V´azquez, and C. Castillo-V´azquez,
“Impact of relay placement on diversity order in adaptive selective DF relay-assisted FSO communications,” Opt. Express 23(3), 2600–2617, 2015 (Impact factor 3.488, 9/86 Optics Q1 JCR 2013).
• A. Garc´ıa-Zambrana, R. Boluda-Ruiz, C. Castillo-V´azquez, and B. Castillo-V´azquez,
“Transmit alternate laser selection with time diversity for FSO communications,” Opt.
Express 22(20), 23,861–23,874, 2014 (Impact factor 3.488, 9/86 Optics Q1 JCR 2013).
• R. Boluda-Ruiz, A. Garc´ıa-Zambrana, C. Castillo-V´azquez, and B. Castillo-V´azquez,
“Adaptive selective relaying in cooperative free-space optical systems over atmospheric
D.2. PROJECTS 135