Document is current
Any future updates will be listed below
-
Authors
Feng, Zhou
Kefeng, Guo https://orcid.org/0000-0002-7535-2057
Jian, Cheng
Sunder Ali, Khowaja
Kapal, Dev
Reddy, Gadekallu Thippa
Hussam Al, Hamadi
-
Funding
Funding for this research was provided by:
National Key Research and Development Program of China (2021QY1303)
National Science Foundation of China (62301473)
Jiangsu Province Industry-University-Research Co-operation Project (BY20231068)
Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions (2023JSJG399)
- License Information
-
More Information
Article History
Received: 13 June 2024
Accepted: 30 September 2024
First Online: 19 December 2024
Declarations
:
: There are no conflicts of interest.
: By considering (), the first task is to derive the expression of and . In the following analysis, the detailed expressions for these two factors will be given, respectively.At the very beginning, the expression for the will be obtained. As discussed in the system model, proposed HAP selection scheme is utilized in the link, and thus, the OP for the first time slot is given aswherewhere represents the OP for the -th by decrypting the common signal and denotes the OP for the -th by deciphering the private signal.With the help of () and (), can be derived asThen, through the similar method for obtaining , the detailed expression for can be obtained asAfter these steps, by inserting () and () into (), will be obtained. Next, by submitting () into (), will be obtained.The second thing is to obtain the expression of , in what follows, will be derived.From (), has the following expression aswhere .From (A5), has an expression asFrom (A6), we realize that the serious thing is to derive the CDF of . With the help of () and (), can be rewritten aswhere , , and .Then, by using (), () and () can be derived.Next, by inserting () and () into (A6), can be rewritten asIt is a pity that, doing the best efforts of ours, (A8) cannot be obtained through the regular way, thus, we use the Gaussian–Chebyshev quadrature in [], and has an expression asThe next step is to submit (A9) into (A5), and the expression for will be derived.At last, by inserting and into (), after several calculating steps, the SOP will be obtained.The proof is over.
