On Performance Analysis of Retransmission Schemes with Fading Channels

Abstract: Future wireless communication systems and services bring increased performance demands, with respect to data-rate(s), reliable communication, (stochastic) real-time guarantees, and more. In this context, not only new communication schemes are needed, but also more capable performance analysis methods are essential. Digital wireless communication systems convey information (digital messages, as data packets) inherently susceptible to errors when communicated. In this respect, fading channels, receiver noise, and interference, are often the main causes of errors. State-of-the-art wireless systems use, e.g., retransmissions (and channel coding) to correct possible remaining errors in communicated message. Retransmissions of erroneous messages are generally known, under the umbrella-term, as automatic repeat request. Adopting a modern terminology (see Chapter 2.2), the three main schemes are here denoted; automatic repeat request (ARQ), repetition redundancy hybrid-ARQ (RR-HARQ), and incremental redundancy hybrid-ARQ (IR-HARQ). There are at least three factors that motivate further performance studies of the ARQ-, RR-, and IR-schemes. First, many commercially important and extensively deployed wireless systems, e.g. cellular systems, use those (H)ARQ-schemes as core system components. Second, those schemes are often integrated with various (recently invented) communication schemes, such as multiple-antenna systems, which promote the need of further studies. Third, the information theoretically-based performance characterization of those (H)ARQ-schemes is, in our view, only in its infancy, and only a few closed-form expressions for very basic (H)ARQ-cases exists in the literature. The thesis deals, on a high level, with the problem of developing performance analysis methods for (H)ARQ-schemes, and, on a more detailed level, studying particularly important (H)ARQ-cases, i.e. with respect to (wrt) (H)ARQ-scheme, fading statistics, antenna-scheme, etc. In doing so, the thesis addresses tools and models that support, ease, or strengthen the analysis.We start our study with a basic throughput analysis of (H)ARQ (Chapter 4). A general throughput expression for HARQ is given in terms of the Laplace-transform (LT) for the probability density function (pdf) of a so called effective-channel. Here, the effective-channel represents the signal-to-noise-ratio (SNR), or mutual information (MI), after signal processing. We then focus on some important (H)ARQ-cases and give closed-form throughput expressions in a general diversity (GD) channel, accounting for space-time-block coding (STC), maximal ratio combining (MRC), and Nakagami-m fading. The throughput of (H)ARQ can, in many cases, be maximized by tuning the initial transmission rate. However, analytical throughput optimization has proven challenging to solve even for the simplest (H)ARQ-cases. We propose a parametric optimization approach, based on judiciously chosen parameter, that allows expressions for the optimal throughput, and the optimal rate point, to be given in closed-forms (Chapter 5). The method is demonstrated for several important, but previously not handled, (H)ARQ-cases. An inherent assumption in this thesis, shared with many other works in wireless communication analysis, is the assumption of that the average symbol MI equals the additive white Gaussian noise (AWGN) channel capacity. The underlying assumption is that the communication symbol can be modeled as an independent and identically distributed (iid) complex Gaussian random variable (r.v). However, practical systems use discrete modulation, not a continuous r.v. Quadrature amplitude modulation (QAM) is the most common (discrete) modulation format in communication systems. Unfortunately, QAM exhibits an asymptotic 1.53 dB SNR-gap relative to the AWGN channel capacity. We substantiate the assumption, of modeling the communication signal as iid complex Gaussian, and close the SNR-shaping-gap, by proposing a novel modulation framework inspired from packing arrangements (spiral-phyllotaxis) among plants (Chapter 6). Much work on wireless performance analysis focus on specialized fading channel gain models, such as exponentially- or gamma-distributed fading. We introduce the idea of a matrix exponential (ME) distributed effective channel SNR (Chapter 7). The ME-distribution is dense on the positive axis, and includes the exponential- and gamma-distribution as special cases. With the ME-distributed channel at hand, we develop an overall ME-distribution-based framework that simplifies the performance analysis and directly express performance measures in the ME-distributed (effective) channel parameters. It has proven hard to analyze (H)ARQ with interference via standard methods, and only special cases have previously been handled successfully. With the ME-distribution-based performance analysis framework, we can now analyze interferers with ME-distributed SNRs. Numerous closed-form throughput expressions are also given in terms of ME-distribution-based channels. Up to this point, the performance measure of choice has been throughput. However, communication systems may impose delay requirements. For this purpose, the effective capacity, giving an indication of communication rate for a given maximum delay and delay violation probability, is a more suitable performance measure. We formulate a very general retransmission system model (allowing for multiple transmissions, multiple communication modes, and multiple rate increments), going beyond classical ARQ-, RR-, and IR-models, and develop a powerful recurrence-based effective capacity performance analysis framework (Chapter 8).Thus, to summarize on a high-level, we introduce a simplifying LT-based performance analysis framework, develop a powerful auxiliary-parameterized throughput optimization method, propose a novel AWGN channel capacity approaching (golden angle) modulation scheme, introduce the ME-distributed channel, develop the ME-distribution-based performance analysis framework, design a highly general retransmission system model, and propose a recurrence-based (effective capacity) performance analysis framework. Throughout the thesis, numerous new closed-form performance expressions are given built on the tools and models introduced in the preceding chapters.