Secrecy Mutual Information of the Independent and Identically Distributed Nakagami-q Fading SIMO Channel

ABSTRACT

In this paper, we consider an independent and identically distributed Nakagami-$q$fading single-input multiple-output (SIMO) channel, where the transmitter sends some confidential message to the legitimate receiver in the presence of an eavesdropper. Both the receiver and the eavesdropper have multiple antennas. We formulated the probability of non-zero secrecy mutual information, secure outage probability, and ergodic secrecy mutual information for the SIMO wireless communication system. The calculations have been carried out using small limit argument approximation on zeroth-order modified Bessel function of first kind. This approximation provides decent results in the low signal-to-noise-ratio (SNR) regime. In the low-SNR regime, either the transmission power is small or the bandwidth is large. In either case, it is difficult for an eavesdropper to detect the signals in this regime. We present that in the presence of fading, positive secrecy mutual information is achievable even when the eavesdropper has better SNR than the main channel. We also found in our work that at low-SNR regime, the effect of number of eavesdropper's channel on average secrecy mutual information is almost negligible.

KEYWORDS:

• Eavesdropper channel
• Ergodic secrecy mutual information
• Nakagami-q
• Main channel
• Positive secrecy mutual information
• Secure outage probability

ACKNOWLEDGMENT

The authors would like to thank Md. Zahurul I. Sarkar, Rajshahi University of Engineering and Technology, for his helpful comments and suggestions of this work.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Md. Sohidul Islam

Md. Sohidul Islam received his BSc degree in computer engineering from American International University-Bangladesh (AIUB) and MS degree on telecommunication engineering from East West University (EWU), Bangladesh in 2007 and 2010, respectively. Currently, he is a PhD student in the Islamic University of Technology (IUT). His research interest includes wireless information-theoretic securities, secrecy capacity, wireless communications, computer networks, and quantum communications.

Mohammad Rakibul Islam

Mohammad Rakibul Islam received the BSc engineering degree and MSc engineering degree in electrical and electronics engineering from Bangladesh University of Engineering and Technology (BUET), Bangladesh in 1998 and 2004, respectively. He also received MBA degree in marketing from the Institute of Business Administration (IBA) under the University of Dhaka in 2006. He received his PhD degree in the department of electronics and radio engineering from Kyung Hee University, South Korea in the year 2010. He joined the department of electrical and electronics engineering at Islamic University of Technology (IUT) as a faculty in 1999 and is serving as a professor there. His research interests include cooperative technique for wireless sensor networks, LDPC and QC-LDPC codes, secrecy capacity, and other wireless applications.

E-mail: [email protected]