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

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

Beamforming in Two-Way Fixed Gain Amplify-and-Forward Relay Systems with CCI

We analyze the outage performance of a two-way fixed gain amplify-and-forward (AF) relay system with beamforming, arbitrary antenna correlation, and co-channel interference (CCI). Assuming CCI at the relay, we derive the exact individual user outage probability in closed-form. Additionally, while neglecting CCI, we also investigate the system outage probability of the considered network, which is declared if any of the two users is in transmission outage. Our results indicate that in this system, the position of the relay plays an important role in determining the user as well as the system outage probability via such parameters as signal-to-noise imbalance, antenna configuration, spatial correlation, and CCI power. To render further insights into the effect of antenna correlation and CCI on the diversity and array gains, an asymptotic expression which tightly converges to exact results is also derived.Comment: Accepted for presentation on IEEE International Conference on Communications (ICC 2012), Ottawa, Canada, June 201

Iterative Deterministic Equivalents for the Performance Analysis of Communication Systems

In this article, we introduce iterative deterministic equivalents as a novel technique for the performance analysis of communication systems whose channels are modeled by complex combinations of independent random matrices. This technique extends the deterministic equivalent approach for the study of functionals of large random matrices to a broader class of random matrix models which naturally arise as channel models in wireless communications. We present two specific applications: First, we consider a multi-hop amplify-and-forward (AF) MIMO relay channel with noise at each stage and derive deterministic approximations of the mutual information after the Kth hop. Second, we study a MIMO multiple access channel (MAC) where the channel between each transmitter and the receiver is represented by the double-scattering channel model. We provide deterministic approximations of the mutual information, the signal-to-interference-plus-noise ratio (SINR) and sum-rate with minimum-mean-square-error (MMSE) detection and derive the asymptotically optimal precoding matrices. In both scenarios, the approximations can be computed by simple and provably converging fixed-point algorithms and are shown to be almost surely tight in the limit when the number of antennas at each node grows infinitely large. Simulations suggest that the approximations are accurate for realistic system dimensions. The technique of iterative deterministic equivalents can be easily extended to other channel models of interest and is, therefore, also a new contribution to the field of random matrix theory.Comment: submitted to the IEEE Transactions on Information Theory, 43 pages, 4 figure

Outage Probability of Dual-Hop Multiple Antenna AF Relaying Systems with Interference

This paper presents an analytical investigation on the outage performance of dual-hop multiple antenna amplify-and-forward relaying systems in the presence of interference. For both the fixed-gain and variable-gain relaying schemes, exact analytical expressions for the outage probability of the systems are derived. Moreover, simple outage probability approximations at the high signal to noise ratio regime are provided, and the diversity order achieved by the systems are characterized. Our results suggest that variable-gain relaying systems always outperform the corresponding fixed-gain relaying systems. In addition, the fixed-gain relaying schemes only achieve diversity order of one, while the achievable diversity order of the variable-gain relaying scheme depends on the location of the multiple antennas.Comment: Accepted to appear in IEEE Transactions on Communication

Adaptive Relay-Selection In Decode-And-Forward Cooperative Systems

In the past few years adaptive decode-and-forward cooperative diversity systems have been studied intensively in literature. Many schemes and protocols have been proposed to enhance the performance of the cooperative systems while trying to alleviate its drawbacks. One of the recent schemes that had been shown to give high improvements in performance is the best-relay selection scheme. In the best-relay selection scheme only one relaying nodes among the relays available in the system is selected to forward the source\u27s message to the destination. The best relay is selected as the relay node that can achieve the highest end-to-end signal-to-noise ratio (snr) at the destination node. Performance improvements have been reported as compared to regular fixed decode-and-forward relaying in which all relays are required to forward the source\u27s message to the destination in terms of spectral efficiency and diversity order. In this thesis, we use simulations to show the improvement in the outage performance of the best-relay selection scheme

Outage Performance Analysis of Multicarrier Relay Selection for Cooperative Networks

In this paper, we analyze the outage performance of two multicarrier relay selection schemes, i.e. bulk and per-subcarrier selections, for two-hop orthogonal frequency-division multiplexing (OFDM) systems. To provide a comprehensive analysis, three forwarding protocols: decode-and-forward (DF), fixed-gain (FG) amplify-and-forward (AF) and variable-gain (VG) AF relay systems are considered. We obtain closed-form approximations for the outage probability and closed-form expressions for the asymptotic outage probability in the high signal-to-noise ratio (SNR) region for all cases. Our analysis is verified by Monte Carlo simulations, and provides an analytical framework for multicarrier systems with relay selection