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

Abstract

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 × 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 nth node will follow a deterministic trajectory through the network governed by the network's maximum Lyapunov exponent, 2) the capacity of the ith eigenchannel at the nth node will follow a deterministic trajectory through the network governed by the network's ith 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.

Information-Theoretic Characterization of MIMO Systems With Multiple Rayleigh Scattering

“…Furthermore, the closed-form expressions that we obtain for the cutoff rate allow us to extensively study the channel behavior and provide interesting insights on the interplay between spatial degrees of freedom (the number of available antennas at either link end), fading degrees of freedom (the number of significant scattering stages), channel coherence, and coding length. It is worth mentioning that a detailed analysis of a MIMO product channel, focused on Lyapunov exponents instead of RCEE, can be found in [24], where the authors analyze an infinite product of finite-sized Rayleigh scattering matrices.…”

Linear Precoding Scheme Design for MIMO Two‐Way Relay Systems with Imperfect Channel State Information

“…There has been extensive theoretical research on the performance improvement of unidirectional MIMO relay system [2,3]. In fact, the MIMO two-way relay system has received great deal of attention recently owing to its high spectrum efficiency [4,5].…”

Random fibonacci sequences and capacity/power scaling in cooperative multihop networks

“…In recent years there has been a concerted effort to understand the behavior of multihop relay systems. For the linear multihop scenario [1], [2] it is known that the capacity of such networks is achieved by employing decode-and-forward (DF) [3] relaying. This can be seen by considering the max-flow min-cut theorem.…”

“…Consequently, the study of multihop AF networks often requires more advanced mathematical tools, e.g., random matrix theory [5] or RDS theory [6]. In [7], [8], multihop AF networks are studied through the formalism of random matrix theory, while [1], [2] studies these networks through the formalism of RDS theory.…”

“…The aim of this paper is to show that much of the analysis performed in [1], which focused on studying AF linear multihop networks through the formalism of RDS theory (and Lyapunov exponents, key observable studied in RDS theory), can be extended to a certain class of AF network that possesses the nonlinear topology depicted in Fig. 1.…”