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

Enhancing Physical Layer Security in AF Relay Assisted Multi-Carrier Wireless Transmission

In this paper, we study the physical layer security (PLS) problem in the dual hop orthogonal frequency division multiplexing (OFDM) based wireless communication system. First, we consider a single user single relay system and study a joint power optimization problem at the source and relay subject to individual power constraint at the two nodes. The aim is to maximize the end to end secrecy rate with optimal power allocation over different sub-carriers. Later, we consider a more general multi-user multi-relay scenario. Under high SNR approximation for end to end secrecy rate, an optimization problem is formulated to jointly optimize power allocation at the BS, the relay selection, sub-carrier assignment to users and the power loading at each of the relaying node. The target is to maximize the overall security of the system subject to independent power budget limits at each transmitting node and the OFDMA based exclusive sub-carrier allocation constraints. A joint optimization solution is obtained through duality theory. Dual decomposition allows to exploit convex optimization techniques to find the power loading at the source and relay nodes. Further, an optimization for power loading at relaying nodes along with relay selection and sub carrier assignment for the fixed power allocation at the BS is also studied. Lastly, a sub-optimal scheme that explores joint power allocation at all transmitting nodes for the fixed subcarrier allocation and relay assignment is investigated. Finally, simulation results are presented to validate the performance of the proposed schemes.Comment: 10 pages, 7 figures, accepted in Transactions on Emerging Telecommunications Technologies (ETT), formerly known as European Transactions on Telecommunications (ETT

Performance Analysis of Optimal Single Stream Beamforming in MIMO Dual-Hop AF Systems

This paper investigates the performance of optimal single stream beamforming schemes in multiple-input multiple-output (MIMO) dual-hop amplify-and-forward (AF) systems. Assuming channel state information is not available at the source and relay, the optimal transmit and receive beamforming vectors are computed at the destination, and the transmit beamforming vector is sent to the transmitter via a dedicated feedback link. Then, a set of new closed-form expressions for the statistical properties of the maximum eigenvalue of the resultant channel is derived, i.e., the cumulative density function (cdf), probability density function (pdf) and general moments, as well as the first order asymptotic expansion and asymptotic large dimension approximations. These analytical expressions are then applied to study three important performance metrics of the system, i.e., outage probability, average symbol error rate and ergodic capacity. In addition, more detailed treatments are provided for some important special cases, e.g., when the number of antennas at one of the nodes is one or large, simple and insightful expressions for the key parameters such as diversity order and array gain of the system are derived. With the analytical results, the joint impact of source, relay and destination antenna numbers on the system performance is addressed, and the performance of optimal beamforming schemes and orthogonal space-time block-coding (OSTBC) schemes are compared. Results reveal that the number of antennas at the relay has a great impact on how the numbers of antennas at the source and destination contribute to the system performance, and optimal beamforming not only achieves the same maximum diversity order as OSTBC, but also provides significant power gains over OSTBC.Comment: to appear in IEEE Journal on Selected Areas in Communications special issue on Theories and Methods for Advanced Wireless Relay