Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

In this paper, we present a novel framework that can be used to study the capacity and power scaling properties of linear multiple-input multiple-output (MIMO) $d\times d$ antenna amplify-and-forward (AF) relay networks. In particular, we model these networks as random dynamical systems (RDS) and calculate their $d$ Lyapunov exponents. Our analysis can be applied to systems with any per-hop channel fading distribution, although in this contribution we focus on Rayleigh fading. Our main results are twofold: 1) the total transmit power at the $n$th node will follow a deterministic trajectory through the network governed by the network's maximum Lyapunov exponent, 2) the capacity of the $i$th eigenchannel at the $n$th node will follow a deterministic trajectory through the network governed by the network's $i$th Lyapunov exponent. Before concluding, we concentrate on some applications of our results. In particular, we show how the Lyapunov exponents are intimately related to the rate at which the eigenchannel capacities diverge from each other, and how this relates to the amplification strategy and number of antennas at each relay. We also use them to determine the extra cost in power associated with each extra multiplexed data stream.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Transactions on Information Theor

Performance analysis of relay-aided wireless communication systems

Relay-aided networks have been proved to be cost-efficient solutions for wireless communications in respect of high data rates, enhanced spectrum efficiency and improved signal coverage. In the past decade, relaying techniques have been written into standards of modern wireless communications and significantly improve the quality of service (QoS) in wireless communications. In order to satisfy exponentially increased demands for data rates and wireless connectivities, various novel techniques for wireless communications have been proposed in recent years, which have brought significant challenges for the performance analysis of relaying networks. For the purpose of more practical investigations into relaying systems, researchers should not only analyse the relays employing novel techniques but also attach more importance to complex environments of wireless communications. With these objectives in mind, in this thesis, in-depth investigations into system performance for relay-assisted wireless communications are detailed. Firstly, the theoretic reliability of dual-hop amplify-and-forward (AF) systems over generalised η-μ and κ-μ fading channels are investigated using Gallager’s error exponents. These two versatile channel models can encompass a number of popular fading channels such as Rayleigh, Rician, Nakagami-m, Hoyt and one-sided Gaussian fading channels. We derive new analytical expressions for the probability distribution function (pdf) of the end-to-end signal-to-noise-ratio (SNR) of the system. These analytical expressions are then applied to analyse the system performance through the study of Gallager’s exponents, which are classical tight bounds of error exponents and present the trade-off between the practical information rate and the reliability of communication. Two types of Gallager’s exponents, namely the random coding error exponent (RCEE) and the expurgated error exponent, are studied. Based on the newly derived analytical expressions, we provide an efficient method to compute the required codeword length to achieve a predefined upper bound of error probability. In addition, the analytical expressions are derived for the cut-off rate and ergodic capacity of the system. Moreover, simplified expressions are presented at the high SNR regime. Secondly, the performance of a dual-hop amplify-and-forward (AF) multi-antenna relaying system over complex Gaussian channels is investigated. Three classical receiving strategies, i.e. the maximal-ratio combining (MRC), zero-forcing (ZF) and minimum mean square error (MMSE) are employed in the relay to mitigate the impact of co-channel interference (CCI), which follows the Poisson point process (PPP). We derive the exact analytical expressions of the capacities for this system in the infinite-area interference environment and the asymptotic analytical expressions for the lower bounds of capacities in the limited-area interference scenario. By computing the numerical results and the Monte Carlo simulation, we can observe the effect of relay processing schemes under different interference regimes. In the end, the non-orthogonal multiple access (NOMA) technique is introduced to relaying systems, which exploits multiplexing in the power domain. Order statistics are applied in this part to analyse the performances of ordered users. The randomness of both channel fading and path loss are taken into consideration. In addition to the exact analytical expressions, asymptotic expressions at high-SNR regimes are provided, which clearly show the effects of NOMA techniques using at relaying systems