Switching-Based Cooperative Decode-and-Forward Relaying for Hybrid FSO/RF Networks

Shubha Sharma; A. S. Madhukumar; Swaminathan R.

doi:10.1364/JOCN.11.000267

Journal of Optical Communications and Networking
Vol. 11,
Issue 6,
pp. 267-281
(2019)
•https://doi.org/10.1364/JOCN.11.000267

Switching-Based Cooperative Decode-and-Forward Relaying for Hybrid FSO/RF Networks

Shubha Sharma, A. S. Madhukumar, and Swaminathan R.

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Shubha Sharma, A. S. Madhukumar, and Swaminathan R., "Switching-Based Cooperative Decode-and-Forward Relaying for Hybrid FSO/RF Networks," J. Opt. Commun. Netw. 11, 267-281 (2019)

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Abstract

In this paper, we propose a switching scheme for a hybrid free-space optical (FSO)/radio frequency (RF) system with a selective decode-and-forward (DF) relay network. Specifically, the system transmits over FSO channels when the instantaneous signal-to-noise ratio (SNR) at the FSO receiver is greater than the threshold SNR. If the SNR drops below the threshold, the system switches and transmits over RF channels. The exact outage probability and average symbol error rate (SER) expressions are derived for a selective DF relay network with maximal ratio combining (MRC) assumed at the destination. In addition, the asymptotic outage and SER expressions with a lower computational complexity are derived and the diversity order is determined. The optimum value of the threshold SNR, which satisfies the target SER, has been calculated numerically for the proposed switching scheme. The theoretical results, which are validated by Monte Carlo simulations, show that the proposed switching scheme for a cooperative hybrid FSO/RF system drastically improves the performance compared to that of a single-hop (SH) switching-based hybrid FSO/RF and cooperative FSO systems.

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$A^{j} ≜ \frac{1}{2 Γ (α_{j}) Γ (β_{j})}$	$R^{j} ≜ α_{j}, β_{j}$	$A_{n_{1}} ≜ A_{1}^{SD} A_{1}^{RD} Γ (\frac{α_{RD}}{2} + 1) \frac{1}{n_{1}!}$	$J_{j} ≜ \frac{1}{Γ (α_{j}) Γ (β_{j})} \frac{π}{2 \sin (π (α_{j} - β_{j}))} {(α_{j} β_{j} / \sqrt{{\bar{γ}}_{j}})}^{(\frac{α_{j} + β_{j}}{2})}$
$A_{1}^{j} ≜ \frac{2^{α_{j} + β_{j}}}{4 π Γ (α_{j}) Γ (β_{j})}$	$v_{j}^{f} ≜ \frac{{(α_{j} β_{j})}^{2}}{16 {\bar{γ}}_{j}^{f}}$	$B_{1}^{j} ≜ \frac{α_{j}}{2}, \frac{α_{j} + 1}{2}, \frac{β_{j}}{2}, \frac{β_{j} + 1}{2}$	$J_{1 n}^{j} ≜ \frac{1}{Γ (n - (α_{j} - β_{j}) + 1) n!} {(α_{j} β_{j} / \sqrt{{\bar{γ}}_{j}})}^{(2 n - (α_{j} - β_{j})) / 2}$
$A_{n_{4}} ≜ \frac{{(- 1)}^{n_{4}} D^{2 n_{4} + 1}}{n_{4}! (2 n_{4} + 1)}$	$w_{j} ≜ \frac{m_{j}}{{\bar{γ}}_{j}^{r}}$	$B_{2, n_{1}}^{j} ≜ \frac{α_{j}}{2} + n_{1}, \frac{α_{j} + 1}{2}$ , $\frac{β_{j}}{2}, \frac{β_{j} + 1}{2}$	$J_{2 n}^{j} ≜ \frac{1}{Γ (n + (α_{j} - β_{j}) + 1) n!} {(α_{j} β_{j} / \sqrt{{\bar{γ}}_{j}})}^{(2 n + (α_{j} - β_{j})) / 2}$
$C_{k_{1}}^{m} ≜ m_{SD} + k_{1}$	$c ≜ \frac{α_{RD}}{2} + 1$	$μ_{1 n}^{j} ≜ \frac{2 n - (α_{j} - β_{j})}{4} + \frac{α_{j} + β_{j}}{4}$	$C_{n_{2}}^{k_{1}} ≜ \frac{w_{SD}^{- k_{1}} w_{RD}^{m_{RD} + n_{2}}}{Γ (m_{SD}) Γ (m_{RD})} \frac{{(- 1)}^{n_{2} + k_{1}}}{n_{2}! (m_{RD} + n_{2})} (\begin{matrix} m_{RD} + n_{2} \\ k_{1} \end{matrix})$
$C_{n_{2}, k_{1}}^{m} ≜ m_{RD} + n_{2} - k_{1}$	$c_{n_{1}} ≜ μ_{g, n}^{SD} + n_{1}$	$μ_{2 n}^{j} ≜ \frac{2 n + (α_{j} - β_{j})}{4} + \frac{α_{j} + β_{j}}{4}$	$C_{n_{2}, k_{1}}^{m, p_{1}} = (C_{n_{2}, k_{1}}^{m} + p_{1})$ , $ℓ_{11} = 1$ , $ℓ_{12} = - 1$

FSO Parameter	Symbol	Value
Wavelength	$λ_{1}$	1.55 μm
Transmit power	$P_{j}^{f}$	50 mW
Responsivity	$η$	$0.5 \frac{A}{W}$
Noise variance	$σ_{1}^{2}$	$10^{- 14}$
RF Parameter	Symbol	Value
Carrier frequency	$f_{c}$	60 GHz
Transmit power	$P_{j}^{r}$	10 mW
Transmit antenna gain	$G_{t}$	44 dBi
Receive antenna gain	$G_{r}$	44 dBi
Attenuation (oxygen)	$α_{oxy}$	15.1 dB/km
Fading severity parameter	$m$	5
Noise power spectral density	$N_{o}$	$- 114 dBm / MHz$
Receiver noise figure	$N_{f}$	5 dB
Weather-dependent parameters of FSO and RF channels
Weather conditions	$α_{1}$ (dB/km)	$α_{rain}$ (dB/km)	$C_{n}^{2}$ ( $m^{- \frac{2}{3}}$ )
Clear air	0.43	0	$5 \times 10^{- 14}$
Haze	4.2	0	$1.7 \times 10^{- 14}$
Moderate rain	5.8	5.6	$5 \times 10^{- 15}$

$l_{3, 1, n}^{i} ≜ J_{1, n}^{i} {(γ_{th}^{f})}^{μ_{1, n}^{i}}$	$B_{4, 1, n}^{j, i} ≜ B_{1}^{j}, - μ_{1, n}^{i}$	$B_{5, 3, n}^{i} ≜ 1 - μ_{1, n}^{i} - (n_{4} + \frac{1}{2}), 1$	$B_{7, 3, n}^{j} ≜ - μ_{1, n}^{j} - n_{4} - \frac{1}{2}, - 1, 0$
$l_{3, 2, n}^{i} ≜ - J_{2, n}^{i} {(γ_{th}^{f})}^{μ_{2, n}^{i}}$	$B_{4, 2, n}^{j, i} ≜ B_{1}^{j}, - μ_{2, n}^{i}$	$B_{5, 4, n}^{i} ≜ 1 - μ_{2, n}^{i} - (n_{4} + \frac{1}{2}), 1$	$B_{7, 4, n}^{j} ≜ - μ_{2, n}^{j} - n_{4} - \frac{1}{2}, - 1, 0$
$l_{3, 3, n}^{i} ≜ - \sum_{n_{4} = 0}^{\infty} \frac{2 A_{n_{4}}}{\sqrt{π}} J_{1, n}^{i} {(γ_{th}^{f})}^{μ_{1, n}^{i} + n_{4} + \frac{1}{2}}$	$B_{5, 1, n}^{i} ≜ 1 - μ_{1, n}^{i}, 1$	$B_{6, 3, n}^{j, i} ≜ B_{1}^{j}, 0, - (μ_{1, n}^{i} - n_{4} - \frac{1}{2})$	$B_{8, 1, n}^{j, i} ≜ B_{2}^{j} - 1, 0, - 1, - μ_{1, n}^{i} - 1$
$l_{3, 4, n}^{i} ≜ \sum_{n_{4} = 0}^{\infty} \frac{2 A_{n_{4}}}{\sqrt{π}} J_{2, n}^{i} {(γ_{th}^{f})}^{μ_{2, n}^{i} + n_{4} + \frac{1}{2}}$	$B_{5, 2, n}^{i} ≜ 1 - μ_{2, n}^{i}, 1$	$B_{6, 4, n}^{j, i} ≜ B_{1}^{j}, 0, - (μ_{2, n}^{i} + n_{4} + \frac{1}{2})$	$B_{8, 2, n}^{j, i} ≜ B_{2}^{j} - 1, 0, - 1, - μ_{2, n}^{i} - 1$
$B_{3, 1, n}^{i} ≜ 1, 1 - μ_{1, n}^{i}, - μ_{1, n}^{i} + \frac{1}{2}$	$B_{6, 1, n}^{j, i} ≜ B_{1}^{j}, 0, - μ_{1, n}^{i}$	$B_{71, n}^{SD} ≜ - μ_{1, n}^{SD}, - 1, 0$	$B_{83, n}^{RD, SD} ≜ B_{2}^{RD} - 1, 0, - 1, - μ_{1, n}^{SD} - n_{4} - \frac{3}{2}$
$B_{3, 2, n}^{i} ≜ 1, 1 - μ_{2, n}^{i}, - μ_{2, n}^{i} + \frac{1}{2}$	$B_{6, 2, n}^{j, i} ≜ B_{1}^{j}, 0, - μ_{2, n}^{i}$	$B_{72, n}^{SD} ≜ - μ_{2, n}^{SD}, - 1, 0$	$B_{84, n}^{RD, SD} ≜ B_{2}^{RD} - 1, 0, - 1, - μ_{2, n}^{SD} - n_{4} - \frac{3}{2}$

$A^{j} ≜ \frac{1}{2 Γ (α_{j}) Γ (β_{j})}$	$R^{j} ≜ α_{j}, β_{j}$	$A_{n_{1}} ≜ A_{1}^{SD} A_{1}^{RD} Γ (\frac{α_{RD}}{2} + 1) \frac{1}{n_{1}!}$	$J_{j} ≜ \frac{1}{Γ (α_{j}) Γ (β_{j})} \frac{π}{2 \sin (π (α_{j} - β_{j}))} {(α_{j} β_{j} / \sqrt{{\bar{γ}}_{j}})}^{(\frac{α_{j} + β_{j}}{2})}$
$A_{1}^{j} ≜ \frac{2^{α_{j} + β_{j}}}{4 π Γ (α_{j}) Γ (β_{j})}$	$v_{j}^{f} ≜ \frac{{(α_{j} β_{j})}^{2}}{16 {\bar{γ}}_{j}^{f}}$	$B_{1}^{j} ≜ \frac{α_{j}}{2}, \frac{α_{j} + 1}{2}, \frac{β_{j}}{2}, \frac{β_{j} + 1}{2}$	$J_{1 n}^{j} ≜ \frac{1}{Γ (n - (α_{j} - β_{j}) + 1) n!} {(α_{j} β_{j} / \sqrt{{\bar{γ}}_{j}})}^{(2 n - (α_{j} - β_{j})) / 2}$
$A_{n_{4}} ≜ \frac{{(- 1)}^{n_{4}} D^{2 n_{4} + 1}}{n_{4}! (2 n_{4} + 1)}$	$w_{j} ≜ \frac{m_{j}}{{\bar{γ}}_{j}^{r}}$	$B_{2, n_{1}}^{j} ≜ \frac{α_{j}}{2} + n_{1}, \frac{α_{j} + 1}{2}$ , $\frac{β_{j}}{2}, \frac{β_{j} + 1}{2}$	$J_{2 n}^{j} ≜ \frac{1}{Γ (n + (α_{j} - β_{j}) + 1) n!} {(α_{j} β_{j} / \sqrt{{\bar{γ}}_{j}})}^{(2 n + (α_{j} - β_{j})) / 2}$
$C_{k_{1}}^{m} ≜ m_{SD} + k_{1}$	$c ≜ \frac{α_{RD}}{2} + 1$	$μ_{1 n}^{j} ≜ \frac{2 n - (α_{j} - β_{j})}{4} + \frac{α_{j} + β_{j}}{4}$	$C_{n_{2}}^{k_{1}} ≜ \frac{w_{SD}^{- k_{1}} w_{RD}^{m_{RD} + n_{2}}}{Γ (m_{SD}) Γ (m_{RD})} \frac{{(- 1)}^{n_{2} + k_{1}}}{n_{2}! (m_{RD} + n_{2})} (\begin{matrix} m_{RD} + n_{2} \\ k_{1} \end{matrix})$
$C_{n_{2}, k_{1}}^{m} ≜ m_{RD} + n_{2} - k_{1}$	$c_{n_{1}} ≜ μ_{g, n}^{SD} + n_{1}$	$μ_{2 n}^{j} ≜ \frac{2 n + (α_{j} - β_{j})}{4} + \frac{α_{j} + β_{j}}{4}$	$C_{n_{2}, k_{1}}^{m, p_{1}} = (C_{n_{2}, k_{1}}^{m} + p_{1})$ , $ℓ_{11} = 1$ , $ℓ_{12} = - 1$

FSO Parameter	Symbol	Value
Wavelength	$λ_{1}$	1.55 μm
Transmit power	$P_{j}^{f}$	50 mW
Responsivity	$η$	$0.5 \frac{A}{W}$
Noise variance	$σ_{1}^{2}$	$10^{- 14}$
RF Parameter	Symbol	Value
Carrier frequency	$f_{c}$	60 GHz
Transmit power	$P_{j}^{r}$	10 mW
Transmit antenna gain	$G_{t}$	44 dBi
Receive antenna gain	$G_{r}$	44 dBi
Attenuation (oxygen)	$α_{oxy}$	15.1 dB/km
Fading severity parameter	$m$	5
Noise power spectral density	$N_{o}$	$- 114 dBm / MHz$
Receiver noise figure	$N_{f}$	5 dB
Weather-dependent parameters of FSO and RF channels
Weather conditions	$α_{1}$ (dB/km)	$α_{rain}$ (dB/km)	$C_{n}^{2}$ ( $m^{- \frac{2}{3}}$ )
Clear air	0.43	0	$5 \times 10^{- 14}$
Haze	4.2	0	$1.7 \times 10^{- 14}$
Moderate rain	5.8	5.6	$5 \times 10^{- 15}$

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Equations (60)

Journal of Optical Communications and Networking