Fundamentals of receiver design

This chapter is devoted to MIMO receivers, with special focus on single-user systems and frequency-flat channels (multi-user systems and more general channels will be the subject of the next chapter). We start with a brief discussion of uncoded MIMO systems, describing their optimum (maximum-likelihood, ML) receivers. Since these may exhibit a complexity that makes them unpractical, it is important to seek receivers that achieve a close-to-optimum performance while keeping a moderate complexity: these would remove the practical restriction to small signal constellations or few antennas. Linear receivers and receivers based on the sphere-detection algorithm are examined as possible solutions to the complexity problem. Next, we study iterative processing of received signals. We introduce here the idea of factor graphs. Their use offers a versatile tool, allowing one to categorize in a simple way the approximations on which MIMO receivers and their algorithms are based. In addition, they yield a “natural” way for the description of iterative (turbo) algorithms, and of their convergence properties through the use of EXIT-charts. Using factor graphs, we describe iterative algorithms for the reception of MIMO signals, along with some noniterative schemes that can be easily developed by using the factor-graph machinery.