Massive multiple-input multiple-output MIMO is one of themost promising technologies for the next generation of wirelesscommunication networks because it has the potential to providegame-changing improvements in spectral efficiency SE and energyefficiency EE. This monograph summarizes many years ofresearch insights in a clear and self-contained way and providesthe reader with the necessary knowledge and mathematical toolsto carry out independent research in this area. Starting froma rigorous definition of Massive MIMO, the monograph coversthe important aspects of channel estimation, SE, EE, hardwareefficiency HE, and various practical deployment considerations.From the beginning, a very general, yet tractable, canonical systemmodel with spatial channel correlation is introduced. This modelis used to realistically assess the SE and EE, and is later extendedto also include the impact of hardware impairments. Owing tothis rigorous modeling approach, a lot of classic "wisdom" aboutMassive MIMO, based on too simplistic system models, is shownto be questionable.

https://www.nowpublishers.com/article/DownloadSummary/SIG-093

Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency

Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

https://hal.archives-ouvertes.fr/hal-01242459/document

Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?

This work deals with the topic of information processing over graphs. The presentation is largely self-contained and covers results that relate to the analysis and design of multi-agent networks for the distributed solution of optimization, adaptation, and learning problems from streaming data through localized interactions among agents. The results derived in this work are useful in comparing network topologies against each other, and in comparing networked solutions against centralized or batch implementations. There are many good reasons for the peaked interest in distributed implementations, especially in this day and age when the word "network" has become commonplace whether one is referring to social networks, power networks, transportation networks, biological networks, or other types of networks. Some of these reasons have to do with the benefits of cooperation in terms of improved performance and improved resilience to failure. Other reasons deal with privacy and secrecy considerations where agents may not be comfortable sharing their data with remote fusion centers. In other situations, the data may already be available in dispersed locations, as happens with cloud computing. One may also be interested in learning through data mining from big data sets. Motivated by these considerations, this work examines the limits of performance of distributed solutions and discusses procedures that help bring forth their potential more fully. The presentation adopts a useful statistical framework and derives performance results that elucidate the mean-square stability, convergence, and steady-state behavior of the learning networks. At the same time, the work illustrates how distributed processing over graphs gives rise to some revealing phenomena due to the coupling effect among the agents. These phenomena are discussed in the context of adaptive networks, along with examples from a variety of areas including distributed sensing, intrusion detection, distributed estimation, online adaptation, network system theory, and machine learning.

/pdf/adaptation-learning-and-optimization-over-networks-h3bow27vho.pdf

Adaptation, Learning, and Optimization Over Networks

This paper surveys recent advances related to adaptation, learning, and optimization over networks. Various distributed strategies are discussed that enable a collection of networked agents to interact locally in response to streaming data and to continually learn and adapt to track drifts in the data and models. Under reasonable technical conditions on the data, the adaptive networks are shown to be mean square stable in the slow adaptation regime, and their mean square error performance and convergence rate are characterized in terms of the network topology and data statistical moments. Classical results for single-agent adaptation and learning are recovered as special cases. The performance results presented in this work are useful in comparing network topologies against each other, and in comparing adaptive networks against centralized or batch implementations. The presentation is complemented with various examples linking together results from various domains.

Adaptive Networks

Nature provides splendid examples of real-time learning and adaptation behavior that emerges from highly localized interactions among agents of limited capabilities. For example, schools of fish are remarkably apt at configuring their topologies almost instantly in the face of danger [1]: when a predator arrives, the entire school opens up to let the predator through and then coalesces again into a moving body to continue its schooling behavior. Likewise, in bee swarms, only a small fraction of the agents (about 5%) are informed, and these informed agents are able to guide the entire swarm of bees to their new hive [2]. It is an extraordinary property of biological networks that sophisticated behavior is able to emerge from simple interactions among lower-level agents [3].

Diffusion strategies for adaptation and learning over networks: an examination of distributed strategies and network behavior

The Perron-Frobenius theorem provides a simple characterization of the eigenvectors and eigenvalues of certain types of matrices with nonnegative entries. The importance of the Perron-Frobenius theorem stems from the fact that eigenvalue problems on these types of matrices frequently arise in many different fields of science and engineering. In this article, the authors discuss the applications of this theorem in diverse areas such as steady state behavior of Markov chains, power control in wireless networks, commodity pricing models in economics, population growth models, and Web search engines. The article starts with a review and discussion of the mathematical foundations.

Seunghun Cha

Papers

The Perron-Frobenius theorem: some of its applications