Full length articleEnhancing security in multicasting through correlated Nakagami- fading channels with opportunistic relaying
Introduction
Antenna diversity and the cooperative network with relay selection are the promising techniques for wireless link improvement by mitigating the effects of multipath fading. Now-a-days multicasting is an effective means of group-oriented wireless data transmission such as video-conference, distance education etc. since the open nature of wireless network make it vulnerable to fraud and eavesdropping. The conventional cryptographic schemes are not able to provide a secure framework, hence, the physical layer security is an important approach to achieve information theoretic security in multicasting.
The secure outage probability (SOP) and average secrecy capacity (ASC) were studied in [1] and the authors showed that the correlation degrades the SOP and ASC. A two relay antenna selection (RAS) model over Nakagami- fading channel was analyzed in [2] to show the effect of spatial correlation, fading and antennas on the RAS scheme. In [3], [4], the SOP was studied where the main and the eavesdropper channels were correlated. The authors showed that the correlation is beneficial for medium and high signal to noise ratio (SNR) regime and detrimental for low SNR regime. The adverse effects of correlated shadowing on the secrecy capacity and the secure outage performance over correlated composite Nakagami-/Gamma fading channel were studied in [5].
Secure wireless multicasting in a regenerative decode and forward (DF) relay network with multiple eavesdroppers was analyzed in [6] over Nakagami- fading channel. Authors derived the closed-form expressions for the SOP and ergodic secrecy capacity (ESC) and showed that the secrecy performance can be enhanced by putting more antennas at the base stations. The end-to-end performance of a dual-hop relay network through fading channel was studied in [7] where the novel expressions for the outage probability and average bit error rate (BER) were derived. The closed-from analytical expressions for the ergodic secrecy multicast capacity (ESMC) and the secure outage probability for multicasting (SOPM) were studied in [8] in a dual-hop multicast cellular network with opportunistic relaying where the authors showed that the cooperative diversity provided by the multiple relays enhance the spectral efficiency significantly.
The authors investigated the outage performance of a correlated wireless power cooperative network in [9] and their results showed that the impact of correlation increases the outage probability but the diversity order is completely independent of the correlation. In [10] a three-stage relay selection scheme was proposed. The impact of correlation and outdated DF relay selection over correlated Rayleigh fading channel on the secure outage performance was studied in [11] where the authors derived closed-form analytical expressions for the SOP. A cognitive relay cooperative network was studied in [12] to compare the performance of traditional partial relay selection and decoding threshold-aided optimal relay selection scheme. The authors derived the analytical approximation for the SOP and an asymptotic expression for the high main-to-eavesdropper ratio of a co-operative dual-hop amplify and forward (AF) relay network in [13]. The effect of correlation was also quantified to indicate that the channel correlation is beneficial for full relay selection and detrimental for partial relay selection. The impacts of channel estimation errors and residual hardware impairments on secrecy characteristics with cooperative relaying techniques were analyzed in [14], [15] in terms of outage and intercept probability. The authors showed that outage behavior develops with increasing numbers of source antennas [14] and relay nodes [15].
In [16], a novel channel quality indicator (CQI) feedback reduction technique was proposed for applications in adaptive multicast IPTV services which eliminates the drawbacks of the conventional techniques. The authors showed that the proposed mechanism decreases the amount of CQI feedback messages significantly preserving the system performance. A novel key management protocol was proposed in [17] for secure group-orientated applications in wireless sensor networks. The authors used both unicast and multicast approaches to share the group keys to all the members and found that multicast approach is more appropriate than the unicast approach in terms of delay time, energy efficiency and code size. In [18], [19], [20], some secure beamforming designs were shown in simultaneous wireless information and power transfer (SWIPT) systems. The authors proposed a successive convex approximation robust design scheme [20] and a sequential parametric convex approximation method [18], [19] under various secrecy and energy harvesting constraints considering both perfect and imperfect channel state information.
Therefore the impact of correlation on the information security was analyzed by the authors of [1], [3], [4], [5], but the multicasting and cooperative diversity schemes were not addressed. The authors of [2] investigated the secrecy performance of a cooperative network ignoring the channel correlation. A secure wireless multicasting cooperative scenario was investigated by the authors of [6], [8] but the effect of correlation was neglected. The authors of [7] considered a cooperative network without correlation, security and multicasting. The cooperative diversity in a correlated network was investigated by the authors of [9], [10] neglecting security and multicasting issue. The security in a cooperative network in the presence of channel correlation was analyzed by the authors of [11], [12], [13] but multicasting issue with constant and exponential correlation was ignored. The authors in [14], [15] analyzed secure networks without considering multicasting scenario. Although in [16], a multicast approach was adopted, the authors did not investigate security threats. The authors of [17] used a secret key for maintaining a secure communication, but our proposed information theoretic security approach ensures a secure communication without any key. Although the authors in [18], [19], [20] considered a multiuser SWIPT system, they did not use opportunistic relaying techniques.
From the afore-cited researches, it is noted that the correlation degrades the receive SNR significantly which in turn reduces the channel capacity. However, to the best of authors knowledge, the effects of constant, exponential and arbitrary correlations on the performance of security in multicasting in the presence of multiple eavesdropper is still an open problem. Furthermore, how the performance level of secure wireless multicasting can be maintained reducing the effects of correlations and number of multicast users is not available in the literature yet. Besides, a trade off between the number of relays and multicast users is required to maintain the acceptable security level reducing the effect of correlations, which is still absent in the literature. Therefore, motivated by the importance of security in multicasting and to solve the aforementioned problems, in this paper a secure cooperative framework with best relay selection in the presence of multiple eavesdropper is presented where all the channels are subjected to constant, exponential and arbitrary correlations. The contributions of this paper can be summarized as follows;
At first, we derive the probability density function (PDF) for the best relay selection strategy.
Secondly, using the above PDF, we derive the closed-form analytical expressions for the probability of non-zero secrecy multicast capacity (PNSMC) and SOPM considering constant, exponential and arbitrary correlations to investigate the effects of correlation on the secrecy capacity.
Finally, we quantify the effects of correlations on the secure outage behavior of the cooperative network and propose the technique to minimize the effects of correlations.
The rest of the paper is organized as follows. Section 2 describes the system model. Derivation of PDFs of best relay for constant, exponential and arbitrary correlations are illustrated in Sections 3 PDF of best relay for constantly correlated case, 4 PDF of best relay for exponentially correlated case, 5 PDF of best relay for arbitrarily correlated case respectively. PDFs of multicast and eavesdropper channels are derived in Sections 6 PDF of multicast channels, 7 PDF of eavesdropper channels. Sections 8 Probability of non-zero secrecy multicast capacity, 9 Secure outage probability for multicasting provides derivations of analytical expressions for PNSMC and SOPM. The numerical results are illustrated in Section 10. Finally, the concluding remarks are presented in Section 11.
Section snippets
System model
We consider a dual-hop secure wireless multicast cooperative cellular network as shown in Fig. 1, where a single antenna source, transmits confidential information to a group of destination users through relays in the presence of eavesdroppers. This proposed multicast scheme can ensure a reliable communication among multiple users simultaneously and is applicable for distance learning, video conferencing etc. communication scenarios. In our model, each relay is equipped with single
PDF of best relay for constantly correlated case
The channels between the source and the relays are uncorrelated, hence the PDF of shown in Fig. 3(a) can be expressed as [22, eq. (10)] where , , and is the average SNR of to link. Now the PDF of shown in Fig. 3(b) is given by [22, eq. (12)] where denotes the Confluent Hypergeometric function [22, eq. (13)] defined as and
PDF of best relay for exponentially correlated case
Similar to Eq. (16), the PDF of SNRs between to th relay denoted by is given by where and . Following the expressions of Eqs. (18), (19), the PDF of SNRs between th relay to th user and th relay to th eavesdropper denoted by , are given by [22, eq. (21)] where , , , , , , ,
PDF of best relay for arbitrarily correlated case
Similar to Eq. (16), the PDF of SNRs between to th relay denoted by is given by [22, eq. (36)] where , and is the average SNR of link. Following the expressions of Eqs. (18), (19), the PDF of SNRs between th relay to th user and th relay to th eavesdropper denoted by and , respectively, are given by [22, eq. (36)]
PDF of multicast channels
It should be noted that the multicast channels (i.e. the channel between relays and destination users) and the eavesdropper’s channels (i.e. the channel between relays and eavesdroppers) both are uncorrelated with each other. The channels of two consecutive destination users are also independent. Only correlation occurs in the antennas of a destination user as well as in the antennas of an eavesdropper. It means that the subchannels between a relay and a destination user are correlated.
PDF of eavesdropper channels
Let denotes the maximum SNR of the eavesdropper channels. Since are independent, hence we have and the PDF of is defined as In the following subsections, we have found the expressions for considering the cases of constant, exponential and arbitrary correlation.
Probability of non-zero secrecy multicast capacity
The secrecy multicast capacity is denoted as [29]. Hence the PNSMC is defined as where is obtained from Eqs. (79), (85), (91) in the case of constant, exponential and arbitrary correlations, respectively. Similarly, due to the constant, exponential and arbitrary correlations are represented by Eqs. (97), (103), (109).
Secure outage probability for multicasting
Denoting as the target secrecy rate, the SOPM is defined as where and . The definition signifies that secure communication is possible if .
Numerical results
This section provides the analytical and simulation results for the proposed model. The effects of fading parameter, channel correlations (i.e. constant, exponential and arbitrary correlations) and the diversity provided by the best relay on the secrecy performance of the proposed model are investigated. For the simulation purpose, a correlated Nakagami- fading channel is generated using MATLAB code. The channel is then used to find the security parameters such as PNSMC and SOPM. Finally each
Conclusion
This work focuses on the enhancement of security in wireless multicasting through correlated Nakagami- fading channels using opportunistic relaying technique. The closed-form analytical expression for the PNSMC and SOPM are derived in terms of the numbers of relays, multicast users, eavesdroppers and the coefficients of constant, exponential and arbitrary correlations which helps to understand the insight of how the correlation affects the security performance in multicasting. Moreover, the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
A. S. M. Badrudduza has received his Bachelor of Science (BSc) and Masters of Science (MSc) in Electrical & Electronic Engineering (EEE) from Rajshahi University of Engineering & Technology (RUET), Kajla, Rajshahi-6204, in 2016 and 2019, respectively. From 16 September, 2016 to 22 July, 2017 he was a Lecturer in the department of EEE at Bangladesh Army University of Engineering & Technology(BAUET), Natore, Rajshahi, Bangladesh. From 23 July, 2017 to 29 June, 2020 he was a lecturer in the
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A. S. M. Badrudduza has received his Bachelor of Science (BSc) and Masters of Science (MSc) in Electrical & Electronic Engineering (EEE) from Rajshahi University of Engineering & Technology (RUET), Kajla, Rajshahi-6204, in 2016 and 2019, respectively. From 16 September, 2016 to 22 July, 2017 he was a Lecturer in the department of EEE at Bangladesh Army University of Engineering & Technology(BAUET), Natore, Rajshahi, Bangladesh. From 23 July, 2017 to 29 June, 2020 he was a lecturer in the department of Electronics and Telecommunication Engineering (ETE) at Rajshahi University of Engineering & Technology(RUET). He is now working as an assistant professor in the Department of ETE, RUET since 30 June, 2020. His research interest includes information-theoretic security in multicast, cellular and cooperative networks, physical layer security of RF/FSO and NOMA systems etc. Mr. Badrudduza was a recipient of two EEE Association Awards (Student of the Year Award) from RUET for his outstanding academic performances in the 1st and 4th year examinations while pursuing BSc engineering degree and two Best Paper Awards for two different research papers from IEEE Region 10 Symposium (TENSYMP 2020), and IEEE 3rd International Conference on Telecommunication and Photonics (ICTP 2019).
Md. Zahurul Islam Sarkar has received his BSc and MSc in Electrical & Electronic Engineering (EEE) from Rajshahi University of Engineering & Technology (RUET), Kajla, Rajshahi-6204, in 1996 and 2000, respectively. He received the PhD degree from the Institute of Electronics, Communications and Information Technology, the School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, United Kingdom in 2012. From 02 June, 2015 he is working as a Professor in the Department of EEE, RUET. His current research interests centered around the lightning induced electromagnetic field, random coding error exponent for MIMO channels, interference coordination in cellular networks, multi-user, multi-cell and massive MIMO systems, random matrix theory and compressed sensing, convex optimization and cross-layer optimization, interference alignment for MIMO channels, security in cognitive radio networks and multicasting. Dr. Sarkar was a research assistant with KHU, South Korea in 2007. He was a post-doctorate research fellow with the Queen’s University Belfast (2012) and the University of Edinbrugh (2013). He has been affiliated with IEEE since 2007 and also a member of IEEE communication society since 2008. Besides he is an reviewer of several IEEE transactions and other international journals. He has served as a TPC for many IEEE conferences. Dr. Sarkar was awarded with many best paper awards from IEEE Region 10 Symposium (TENSYMP 2020), 2nd IEEE International Conference on Electrical, Computer and Telecommunication Engineering (ICECTE) 2016, 1st IEEE International Conference on Electrical and Electronic Engineering (ICEEE) 2015, 67th IEEE Vehicular Technology Conference (VTC) 2008-Spring, Singapore etc. He has more than 100 technical papers in his research areas.
Milton Kumar Kundu has received his BSc in Electrical & Electronic Engineering (EEE) from Rajshahi University of Engineering & Technology (RUET), Kajla, Rajshahi-6204, in 2016. He has worked as the Lecturer in the department of EEE at North Bengal International University, Rajshahi, Bangladesh from 20 May, 2017 to 14 February, 2019. He is now working as the Lecturer in the Department of Electrical & Computer Engineering (ECE), RUET since 16 February, 2019. He is also the Advisor of IEEE RUET Industry Applications Society (IAS) Student Branch Chapter. His research interests are centered around the security aspects of cooperative and physical-layer networks and wireless multicasting. Mr. M. K. Kundu has won several awards including the 2nd runner-up award in regional Mathematical Olympiad and EEE Association Award (Student of the Year Award) from RUET for his outstanding academic performances in the 3rd year examinations while pursuing BSc engineering degree. He has also won two Best Paper Awards for two different research papers from IEEE Region 10 Symposium (TENSYMP 2020), and IEEE 3rd International Conference on Telecommunication and Photonics (ICTP 2019).