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The goal of this lecture has been to provide an overview of approaches, in the communications receiver context. Which method is the best in practice? This depends much on the purpose of solving : what error rate can be tolerated, what is the ultimate measure of performance (e.g., frame-error-rate, worst-case complexity, or average complexity), and what computational platform is used. Additionally, the bits in s may be part of a larger code word and different s vectors in that code word may either see the same H (slow fading) or many different realizations of H (fast fading). This complicates the picture, because notions that are important in slow fading (such as spatial diversity) are less important in fast fading, where diversity is provided anyway by time variations. Detection for MIMO has been an active field for more than ten years, and this research will probably continue for some time.