Random Matrix Methods for Wireless Communications

International audienceThis book introduces the field of random matrix theory and particularly of large dimensional random matrix theory from the point of view of their applications to wireless communications. In mathematical terms, the main objective of the book is to provide the reader with the necessary tools and methods to handle wireless communication problems dealing with random matrices. A non-exhaustive list of important results is reviewed, the proofs of which are intended for be profoundly instrumental to provide the reader with both intuition and accurate tools in a step-by-step method. Although multiple approaches are known to deal with problems of random matrices, the book is mostly concerned with two of those: the Stieltjes transform and the free probability approaches. Regarding applications, the book reviews and sometimes extends results of the last decade of random matrix theory for wireless communications. The most relevant of these applications are divided into several topics: system performance considerations, i.e. capacity estimation and optimization in multi-dimensional communication systems (CDMA, MIMO, multi-user, multi-cellular, etc.), and the more recent statistical inference problems, i.e. signal sensing, parameter estimation and system modeling