A Unified Framework for Communications through MIMO Channels

MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) CHANNELS constitute a unified way of modeling a wide range of different physical communication channels, which can then be handled with a compact and elegant vector-matrix notation. The two paradigmatic examples are wireless multi-antenna channels and wireline Digital Subscriber Line (DSL) channels. Research in antenna arrays (also known as smart antennas) dates back to the 1960s. However, the use of multiples antennas at both the transmitter and the receiver, which can be naturally modeled as a MIMO channel, has been recently shown to offer a significant potential increase in capacity. DSL has gained popularity as a broadband access technology capable of reliably delivering high data rates over telephone subscriber lines. A DSL system can be modeled as a communication through a MIMO channel by considering all the copper twisted pairs within a binder as a whole rather than treating each twisted pair independently. This dissertation considers arbitrary MIMO channels regardless of the physical nature of the channels themselves; as a consequence, the obtained results apply to any communication system that can be modeled as such. After an extensive overview of MIMO channels, both fundamental limits and practical communication aspects of such channels are considered. First, the fundamental limits of MIMO channels are studied. An information-theoretic approach is taken to obtain different notions of capacity as a function of the degree of channel knowledge for both single-user and multiuser scenarios. Specifically, a game-theoretic framework is adopted to obtain robust solutions under channel uncertainty. Then, practical communication schemes for MIMO channels are derived for the single-user case or, more exactly, for point-to-point communications (either single-user or multiuser when coordination is possible at both sides of the link). In particular, a joint design of the transmit-receive linear processing (or beamforming) is obtained (assuming a perfect channel knowledge) for systems with either a power constraint or Quality of Service (QoS) constraints. For power-constrained systems, a variety of measures of quality can be defined to optimize the performance. For this purpose, a novel unified framework that generalizes the existing results in the literature is developed based on majorization theory. In particular, the optimal structure of the transmitter and receiver is obtained for a wide family of objective functions that can be used to measure the quality of a communication system. Using this unified framework, the original complicated nonconvex problem with matrix-valued variables simplifies into a much simpler convex problem with scalar variables. With such a simplification, the design problem can be then reformulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved even though closed-form expressions may not exist. Among other results, a closed-form expression for optimum beamforming in terms of minimum average bit error rate (BER) is obtained. For other design criteria, either closed-form solutions are given or practical algorithms are derived within the framework of convex optimization theory. For QoS-constrained systems, although the original problem is a complicated nonconvex problem with matrix-valued variables, with the aid of majorization theory, the problem is reformulated as a simple convex optimization problem with scalar variables. An efficient multi-level water-filling algorithm is given to optimally solve the problem in practice. Finally, the more realistic situation of imperfect channel knowledge due to channel estimation errors is considered. The previous results on the joint transmit-receive design for MIMO channels are then extended in this sense to obtain robust designs.