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On the Effects of Jacks Correlation on the Secrecy Multicast Capacity of MIMO Fading Channels: A Comparative Study

Rezwana Sultana, M. Z. I. Sarker, Md. Sazzad Hossain

Published May 15, 2024• 0 citations
Publisher

Abstract

Abstract A confidential communication over multiple-input multiple-output (MIMO) fading channels is considered, in which a transmitter communicates with a group of receivers in the presence of multiple eavesdroppers. The antenna correlation depends on both the antenna spacing and the angular spectrum of the incoming radio waves. We derive the closed-form analytical expressions of the ergodic secrecy multicast capacity for Rayleigh and Ricean fading MIMO channels considering a linear array with equally spaced antennas and employing the classical Jakes correlation. Then, we compare the performance of Rayleigh and Ricean fading channels showing the effects of fading, antenna correlation and the spacing between antenna elements. Our results show that antenna correlations significantly reduces the ergodic secrecy multicast capacity of Rayleigh as well as Ricean fading MIMO channels and this effect is more severe in the case of Rayleigh fading channel compared to Ricean fading.

DOI
10.21203/rs.3.rs-4382554/v1

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Abstract A confidential communication over multiple-input multiple-output (MIMO) fading channels is considered, in which a transmitter communicates with a group of receivers in the presence of multiple eavesdroppers. The antenna correlation depends on both the antenna spacing and the angular spectrum of the incoming radio waves. We derive the closed-form analytical expressions of the ergodic secrecy multicast capacity for Rayleigh and Ricean fading MIMO channels considering a linear array with equally spaced antennas and employing the classical Jakes correlation. Then, we compare the performance of Rayleigh and Ricean fading channels showing the effects of fading, antenna correlation and the spacing between antenna elements. Our results show that antenna correlations significantly reduces the ergodic secrecy multicast capacity of Rayleigh as well as Ricean fading MIMO channels and this effect is more severe in the case of Rayleigh fading channel compared to Ricean fading.
In a multiple antenna network, correlation among the antennas tends to reduce the system capacity. In this paper, the effect of correlation on the secrecy performance over η - μ fading channel has been analyzed considering a multicast network in the presence of multiple eavesdroppers. Simple closed-form analytical expressions of the ergodic secrecy multicast capacity and the secure outage probability for multicasting are derived to numerically quantify the effect of correlation. The consequence of changing the number of receiving antennas on correlation has been observed and the secrecy performance of some commonly used channels like Gaussian channel, Rayleigh and Nakagami- m fading channels which can be found as a special case of the η - μ fading channel, have also been investigated. The derived expressions are finally verified through Monte-Carlo simulations.
A secure multicasting framework is considered in this paper to investigate the secrecy performance of a single-input multiple-output (SIMO) system in which a single antenna source transmits private message to multiple receivers in the presence of multiple eavesdroppers. All the receivers and eavesdroppers are equipped with multiple antennas. The perfect secrecy is obtained when evasedroppers can not be able to decode any transmitted information. Considering independent and identically distributed (i.i.d) Rician-K fading channels, the mathematical expressions for the probability of non-zero secrecy multicast capacity, the ergodic secrecy multicast capacity and the secure outage probability for multicasting are derived in closed-forms. Numerical results are provided to show the impact of the diversity provided by the multiple antennas at the receivers. In addition, the impact of Rician factor, K on the secrecy capacity and outage behaviour of the proposed multicasting scenario is also demonstrated. The performance analysis includes the Rayleigh fading scenario as a special case of Rician-K fading channel and focuses the performance comparison between Rician-K and Rayleigh fading channels.
In this paper, we consider the problem of transmission of sensitive message in wireless multicast cellular network through identically distributed Nakagami-m fading multiple-input multiple-output (MIMO) channels considering the existence of multiple eavesdroppers. It is assumed that the antennas in the destinations and eavesdroppers are exponentially correlated. Considering channel state information (CSI) at the receiver, the closed-form analytical expressions for the ergodic secrecy multicast capacity (ESMC) and the probability of non zero secrecy multicast capacity (PNSMC) have been derived to investigate the effect of correlation and fading parameter on the proposed model. Numerical results of the derived analytical expressions are presented and demonstrated using Monte-Carlo simulation.
A new closed form expression for the ergodic secrecy capacity with multi-keyhole Multiple-Input Multiple-Output (MIMO) channel has been derived in this paper. Assuming independent and identically distributed (i.i.d.) Rayleigh flat-fading between transmitting and receiving antennas and equal power allocation to each of the transmit antennas, the ergodic secrecy capacity is expressed as a finite sum of weighted Meiger G-functions for ease of calculation. The effect of the number of keyhole on the ergodic secrecy capacity as well as on the receiving antenna is also analyzed in this paper.
In this paper, a wireless multicast scenario is considered in which the transmitter sends a common message to multiple client receivers in the presence of an eavesdropper. We are interested in protecting this common message against eavesdropping. Based on an information-theoretic formulation of the problem, in which the transmitter and the mutually independent multiple client receivers communicate over quasi-static Rayleigh fading channels and an eavesdropper observes their transmissions through another quasi-static Rayleigh fading channel, we define the secrecy-sum capacity in terms of secure outage probability. Moreover, we also present a formulation of ergodic perfect secrecy multicast capacity at which the eavesdropper is unable to decode any information.
This paper focuse on the secrecy performance analysis over correlated κ - μ shadowed fading multicast channels considering a single input multiple output (SIMO) scenario. The proposed network consists of a single antenna source, and multiple receivers and eavesdroppers which are equipped with multiple antennas. The security analysis has been performed by developing a mathematical model and deriving the novel closed-form expressions(CFEs)of the performance matrices such as probability of non-zero secrecy multicast capacity (PNSMC) and secure outage probability for multicasting (SOPM). The secrecy capacity and outage characteristics of the multicast network has been investigated for the simultaneous presence of correlation and shadowing and it is observed that impact of each system parameter can be evaluated perfectly using the derived expressions. Finally, the analytical results has been verified by Monte-Carlo Simulations.