On the design of iterative wireless receivers : the divergence minimization approach to approximate Bayesian inference

The discovery of turbo codes in the 1990s has revolutionized the design of communication systems. Unlike traditional channel codes, they are characterized by a complex, pseudo-random structure which enables datarates close to the channel capacity. The key innovation of turbo codes has been their novel approach to decoding: it consists of two constituent decoders which run alternately several times and exchange information about the transmitted data during this process. It has been observed empirically that this iterative scheme converges with a high probability to the correct solution, despite the lack of any theoretical guarantees. Following the remarkable success of turbo codes, the concept of iterative information processing has also been applied to other tasks of wireless receivers, yielding techniques like code-aided synchronization and iterative detection and decoding. Initially, the proposed algorithms were rather heuristic, but a significant research effort has been invested into the development of a theoretical foundation. An important step has been the derivation of the turbo decoder as an instance of belief propagation (BP), a framework for solving Bayesian inference problems. Unfortunately, it turns out that BP is less suitable for other tasks beyond the channel decoder. For example, using BP for the design of code-aided synchronization schemes, which require the estimation of continuous variables, gives rise to integrals that typically do not admit a closed-form solution. For this class of problems, the expectation-maximization (EM) algorithm has emerged as a better alternative, which however has its own drawbacks. Additionally, high-dimensional detection problems, which arise for example in the context of multi-antenna (MIMO) systems, involve sums with exponentially many terms whose evaluation is practically infeasible. In this thesis, we investigate the design of iterative wireless receivers based on a generic framework for approximate Bayesian inference that has recently been developed in the machine learning community. Its key idea is the conversion of the original summation or integration problem into an equivalent optimization problem, which is then solved approximately by an iterative algorithm. As it consists of the minimization of a divergence measure between the probabilistic system model and a simpler auxiliary distribution, we refer to this approach as divergence minimization (DM). Due to its generality, DM provides the designer with a great deal of flexibility, and it contains specific algorithms like BP and EM as special cases. This thesis begins with a systematic derivation of a combined EMand BP-based receiver, which has been proposed earlier in the literature in a rather ad-hoc way. We then utilize the flexibility of DM for the development of several novel parameter estimation and MIMO detection algorithms, which due to their good performance and low computational complexity are interesting options for practical implementations. Further, this thesis also contributes to the theoretical understanding of iterative methods. In earlier work, the subcomponents were often designed separately and then connected heuristically. In contrast, the virtue of the proposed holistic approach to receiver design is that it does not only specify the individual functional units but also their interactions. In particular, there has been some confusion in the literature on whether the components should exchange extrinsic information as in the turbo decoder, or whether exchanging the full posterior information is preferable. The derivations that are presented in this thesis shed light on this important question.