Impact of Link Parameters and Channel Correlation on the Performance of FSO Systems With the Differential Signaling Technique: errata

Mojtaba Mansour Abadi; Zabih Ghassemlooy; Stanislav Zvanovec; Manav R. Bhatnagar; Mohammad-Ali Khalighi; Yongle Wu

doi:10.1364/JOCN.9.001062

We would like to point out that in our paper [1], the following mistakes need to be corrected.

Page 140, right column, paragraph 1, line 4 should read “Also from the literature [2], we have adopted $Mean (h_{i}) = \exp (2 μ_{h, i} + 2 σ_{h, i}^{2})$ and $Var (h_{i}) = (\exp (4 σ_{h, i}^{2}) - 1) \times \exp (4 μ_{h, i} + 4 σ_{h, i}^{2})$ in order to obtain Eq. (3).”

Also, the derived equations need to be corrected as follows.

On page 140, Eq. (3a) should be corrected to

Mean (y_{1}) = {\begin{matrix} \frac{ϵ_{1} ϕ_{1}}{(1 + ϵ_{1})} & bit 1 \\ ϕ_{1} & Threshold \\ \frac{ϕ_{1}}{(1 + ϵ_{1})} & bit 0 \end{matrix} .

On page 140, Eq. (3b) should be corrected to

Var (y_{1}) = σ_{n, 1}^{2} + [\exp (4 σ_{h, 1}^{2}) - 1] \times {\begin{matrix} {(\frac{2 ϵ_{1} ϕ_{1}}{(1 + ϵ_{1})})}^{2} & bit 1 \\ {(ϕ_{1})}^{2} & Threshold \\ {(\frac{2 ϕ_{1}}{(1 + ϵ_{1})})}^{2} & bit 0 \end{matrix} .

On page 141, Eq. (5a) should be corrected to

Mean (Y) = {\begin{matrix} \frac{2 ϵ_{1} ϕ_{1}}{(1 + ϵ_{1})} - \frac{2 ϕ_{2}}{(1 + ϵ_{2})} & bit 1 \\ ϕ_{1} - ϕ_{2} & Threshold \\ \frac{2 ϕ_{1}}{(1 + ϵ_{1})} - \frac{2 ϵ_{2} ϕ_{2}}{(1 + ϵ_{2})} & bit 0 \end{matrix} .

On page 141, Eq. (5b) should be corrected to

Var (y_{1}) = σ_{n, 1}^{2} + σ_{n, 2}^{2} + [\exp (4 σ_{h, 1}^{2}) - 1] \times {\begin{matrix} {(\frac{2 ϵ_{1} ϕ_{1}}{(1 + ϵ_{1})})}^{2} + {(\frac{2 ϕ_{2}}{(1 + ϵ_{2})})}^{2} - 2 ρ_{1, 2} \frac{4 ϵ_{1} ϕ_{1} ϕ_{2}}{(1 + ϵ_{1}) (1 + ϵ_{2})} & bit 1 \\ {(ϕ_{1})}^{2} + {(ϕ_{2})}^{2} - 2 ρ_{1, 2} ϕ_{1} ϕ_{2} & Threshold \\ {(\frac{2 ϕ_{1}}{(1 + ϵ_{1})})}^{2} + {(\frac{2 ϵ_{2} ϕ_{2}}{(1 + ϵ_{2})})}^{2} - 2 ρ_{1, 2} \frac{4 ϵ_{2} ϕ_{1} ϕ_{2}}{(1 + ϵ_{1}) (1 + ϵ_{2})} & bit 0 \end{matrix} .

On page 141, Eq. (6) should be corrected to

Var (Y_{TL}) = 2 [\exp (4 σ_{h, 1}^{2}) - 1] {(ϕ_{1})}^{2} (1 - ρ_{1,2}) + σ_{n, 1}^{2} + σ_{n, 2}^{2} .

On page 142, Eq. (9a) should be corrected to

Mean (Y_{bit 0}) = 2 ϕ_{1} [\frac{1}{(1 + ϵ_{1})} - \frac{ϵ_{2}}{(1 + ϵ_{2})}] .

On page 141, Eq. (9b) should be corrected to

Mean (Y_{bit 1}) = 2 ϕ_{1} [\frac{ϵ_{1}}{(1 + ϵ_{1})} - \frac{1}{(1 + ϵ_{2})}] .

On page 141, Eq. (9c) should be corrected to

Var (Y_{bit 0}) = 4 [\exp (4 σ_{h, 1}^{2}) - 1] {(ϕ_{1})}^{2} [{(\frac{1}{(1 + ϵ_{1})})}^{2} + {(\frac{ϵ_{2}}{(1 + ϵ_{2})})}^{2} - 2 ρ_{1,2} \frac{ϵ_{2}}{(1 + ϵ_{1}) (1 + ϵ_{2})}] + σ_{n, 1}^{2} + σ_{n, 2}^{2} .

On page 141, Eq. (9d) should be corrected to

Var (Y_{bit 1}) = 4 [\exp (4 σ_{h, 1}^{2}) - 1] {(ϕ_{1})}^{2} [{(\frac{ϵ_{1}}{(1 + ϵ_{1})})}^{2} + {(\frac{1}{(1 + ϵ_{2})})}^{2} - 2 ρ_{1,2} \frac{ϵ_{1}}{(1 + ϵ_{1}) (1 + ϵ_{2})}] + σ_{n, 1}^{2} + σ_{n, 2}^{2} .

All the results and discussions presented in the paper are based on the correct version of the equations.

Acknowledgment

One of the authors, M. Mansour Abadi, has a Ph.D. scholarship from Northumbria University. The work was also supported by the EU FP7 Cost Action IC1101.

Reference

1. M. Mansour Abadi, Z. Ghassemlooy, S. Zvanovec, M. R. Bhatnagar, M.-A. Khalighi, and Y. Wu, “Impact of link parameters and channel correlation on the performance of FSO systems with the differential signaling technique,” J. Opt. Commun. Netw., vol. 9, pp. 138–148, Feb. 2017. [CrossRef]

Impact of Link Parameters and Channel Correlation on the Performance of FSO Systems With the Differential Signaling Technique: errata

Abstract

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Journal of Optical Communications and Networking