A novel equivalent definition of modified Bessel functions for performance analysis of multi-hop wireless communication systems

A statistical model is derived for the equivalent signal-to-noise ratio of the Source-to-Relay-to-Destination (S-R-D) link for Amplify-and-Forward (AF) relaying systems that are subject to block Rayleigh-fading. The probability density function and the cumulated density function of the S-R-D link SNR involve modified Bessel functions of the second kind. Using fractional-calculus mathematics, a novel approach is introduced to rewrite those Bessel functions (and the statistical model of the S-R-D link SNR) in series form using simple elementary functions. Moreover, a statistical characterization of the total receive-SNR at the destination, corresponding to the S-R-D and the S-D link SNR, is provided for a more general relaying scenario in which the destination receives signals from both the relay and the source and processes them using maximum ratio combining (MRC). Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained. The analytical results presented in this paper provide a theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver

Secure Two-Way Transmission via Wireless-Powered Untrusted Relay and External Jammer

In this paper, we propose a two-way secure communication scheme where two transceivers exchange confidential messages via a wireless powered untrusted amplify-and-forward (AF) relay in the presence of an external jammer. We take into account both friendly jamming (FJ) and Gaussian noise jamming (GNJ) scenarios. Based on the time switching (TS) architecture at the relay, the data transmission is done in three phases. In the first phase, both the energy-starved nodes, the untrustworthy relay and the jammer, are charged by non-information radio frequency (RF) signals from the sources. In the second phase, the two sources send their information signals and concurrently, the jammer transmits artificial noise to confuse the curious relay. Finally, the third phase is dedicated to forward a scaled version of the received signal from the relay to the sources. For the proposed secure transmission schemes, we derive new closed-form lower-bound expressions for the ergodic secrecy sum rate (ESSR) in the high signal-to-noise ratio (SNR) regime. We further analyze the asymptotic ESSR to determine the key parameters; the high SNR slope and the high SNR power offset of the jamming based scenarios. To highlight the performance advantage of the proposed FJ, we also examine the scenario of without jamming (WoJ). Finally, numerical examples and discussions are provided to acquire some engineering insights, and to demonstrate the impacts of different system parameters on the secrecy performance of the considered communication scenarios. The numerical results illustrate that the proposed FJ significantly outperforms the traditional one-way communication and the Constellation rotation approach, as well as our proposed benchmarks, the two-way WoJ and GNJ scenarios.Comment: 14 pages, 6 figures, Submitted to IEEE Transactions on Vehicular Technolog

A Simple Cooperative Diversity Method Based on Network Path Selection

Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However most of the proposed solutions require distributed space-time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme, that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of M available relays and then uses this best relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space-time coding for M nodes is required, such as those proposed in [7]. The simplicity of the technique, allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability and efficiency in future 4G wireless systems.Comment: To appear, IEEE JSAC, special issue on 4

On the Multivariate Gamma-Gamma (ΓΓ\Gamma \Gamma) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate $\Gamma \Gamma$ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.Comment: 7 pages, 6 figures, accepted by IEEE Transactions on Vehicular Technolog