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

On the Performance of SR and FR Protocols for OSTBC based AF-MIMO Relay System with Channel and Noise Correlations

This paper proposes selection relaying (SR) protocol for a cooperative multiple-input multiple-output (MIMO) relay system that consists of a direct link between a source and a destination. The system has only receive-side channel state information (CSI), spatially correlated MIMO channels, and the receiver nodes observe spatially correlated noise. The transmit nodes employ orthogonal space-time block codes (OSTBC), whereas the receiver nodes employ optimum minimum mean-square-error (MMSE) detection. The SR protocol, which transmits via the relay only when the direct link between the source and destination is in outage, is compared with the fixed relaying (FR) protocol which always uses the relay. By deriving novel asymptotic expressions of the outage probabilities, it is analytically shown that both protocols provide the same diversity gain. However, the coding gain (CG) of the SR protocol can be much better than that of the FR protocol. In particular, when all MIMO links have the same effective rank, irrespective of its value, the SR protocol provides better CG than the FR scheme if the target information rate is greater than ln2(3) bits per channel use. Simulation results support theoretical analysis and show that the SR scheme can significantly outperform FR method, which may justify the increased complexity due to one-bit feedback requirement in the SR protocol