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Lee Swindlehurst et al., Applications of Array Signal Processing. In: Rama Chellappa and Sergios Theodoridis, editors, Academic Press Library in Signal Processing. Vol 3, Array and Statistical Signal Processing, Chennai: Academic Press, 2014, p. 859-953. ISBN: 978-0-12-411597-2 © Copyright 2014 Elsevier Ltd Academic Press. Author’s personal copy CHAPTER Applications of Array Signal Processing 20 A. Lee Swindlehurst*, Brian D. Jeffs†, Gonzalo Seco-Granados‡, and Jian Li§ *Department of Electrical Engineering and Computer Science, University of California, Irvine, CA, USA †Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT, USA ‡Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain §Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA 3.20.1 Introduction and background The principles behind obtaining information from measuring an acoustic or electro-magnetic field at different points in space have been understood for many years. Techniques for long-baseline optical inter- ferometry were known in the mid-19th century, where widely separated telescopes were proposed for high-resolution astronomical imaging. The idea that direction finding can be performed with two acous- tic sensors has been around at least as long as the physiology of human hearing has been understood. The mathematical duality observed between sampling a signal either uniformly in time or uniformly in space is ultimately just an elegant expression of Einstein’s theory of relativity. However, most of the technical advances in array signal processing have occurred in the last 30 years, with the development and prolif- eration of inexpensive and high-rate analog-to-digital (A/D) converters together with flexible and very powerful digital signal processors (DSPs). These devices have made the chore of collecting data from multiple sensors relatively easy, and helped give birth to the use of sensor arrays in many different areas. Parallel to the advances in hardware that facilitated the construction of sensor array platforms were breakthroughs in the mathematical tools and models used to exploit sensor array data. Finite impulse response (FIR) filter design methods originally developed for time-domain applications were soon applied to uniform linear arrays in implementing digital beamformers. Powerful data-adaptive beam- formers with constrained look directions were conceived and applied with great success in applications where the rejection of strong interference was required. Least-mean square (LMS) and recursive least- squares (RLS) time-adaptive techniques were developed for time-varying scenarios. So-called “blind” adaptive beamforming algorithms were devised that exploited known temporal properties of the desired signal rather than its direction-of-arrival (DOA). For applications where a sensor array was to be used for locating a signal source, for example finding the source’s DOA, one of the key theoretical developments was the parametric vector-space formulation introduced by Schmidt and others in the 1980s. They popularized a vector space signal model with a parameterized array manifold that helped connect problems in array signal processing to advanced estimation theoretic tools such as Maximum Likelihood (ML), Minimum Mean-Square Estimation (MMSE) the Likelihood Ratio Test (LRT) and the Cramér-Rao Bound (CRB). With these Academic Press Library in Signal Processing. http://dx.doi.org/10.1016/B978-0-12-411597-2.00020-5 859 © 2014 Elsevier Ltd. All rights reserved. Author’s personal copy 860 CHAPTER 20 Applications of Array Signal Processing tools, one could rigorously define the meaning of the term “optimal” and performance could be compared against theoretical bounds. Trade-offs between computation and performance led to the development of efficient algorithms that exploited certain types of array geometries. Later, concerns about the fidelity of array manifold models motivated researchers to study more robust designs and to focus on models that exploited properties of the received signals themselves. The driving applications for many of the advances in array signal processing mentioned above have come from military problems involving radar and sonar. For obvious reasons, the military has great interest in the ability of multi-sensor surveillance systems to locate and track multiple “sources of interest” with high resolution. Furthermore, the potential to null co-channel interference through beamforming (or perhaps more precisely, “null-steering”) is a critical advantage gained by using multiple antennas for sensing and communication. The interference mitigation capabilities of antenna arrays and information theoretic analyses promising large capacity gains has given rise to a surge of applications for arrays in multi-input, multi-output (MIMO) wireless communications in the last 15 years. Essentially all current and planned cellular networks and wireless standards rely on the use of antenna arrays for extending range, minimizing transmit power, increasing throughput, and reducing interference. From peering to the edge of the universe with arrays of radio telescopes to probing the structure of the brain using electrode arrays for electroencephalography (EEG), many other applications have benefited from advances in array signal processing. In this chapter, we explore some of the many applications in which array signal processing has proven to be useful. We place emphasis on the word “some” here, since our discussion will not be exhaustive. We will discuss several popular applications across a wide variety of disciplines to indicate the breadth of the field, rather than delve deeply into any one or try to list them all. Our emphasis will be on developing a data model for each application that falls within the common mathematical framework typically assumed in array processing problems. We will spend little time on algorithms, presuming that such material is covered elsewhere in this collection; algorithm issues will only be addressed when the model structure for a given application has unique implications on algorithm choice and implementation. Since radar and wireless communications problems are discussed in extensive detail elsewhere in the book, our discussion of these topics will be relatively brief. 3.20.2 Radar applications We begin with the application area for which array signal processing has had the most long-lasting impact, dating back to at least World War II. Early radar surveillance systems, and even many still in use today, obtain high angular resolution by employing a radar dish that is mechanically steered in order to scan a region of interest. While such slow scanning speeds are suitable for weather or navigation purposes, they are less tolerable in military applications where split-second decisions must be made regarding targets (e.g., missiles) that may be moving at several thousand miles per hour. The advent of electronically scanned phased arrays addressed this problem, and ushered in the era of modern array signal processing. Phased arrays are composed of from a few up to several thousand individual antennas laid out in a line, circle, rectangle or even randomly. Directionality is achieved by the process of beamforming: multiplying the output of each antenna by a complex weight with a properly designed phase (hence the term “phased” array), and then summing these weighted outputs together. The conventional “delay-and-sum” Author’s personal copy 3.20.2 Radar Applications 861 FIGURE 20.1 A phased array radar enclosed in the nose of a fighter jet. beamforming scheme involves choosing the weights to phase delay the individual antenna outputs such that signals from a chosen direction add constructively and those from other directions do not. Since the weights are applied electronically, they can be rapidly changed in order to focus the array in many different directions in a very short period of time. Modern phased arrays can scan an entire hemisphere of directions thousands of times per second. Figures 20.1 and 20.2 show examples of airborne and ground-based phased array radars. For scanning phased arrays, a fixed set of beamforming weights is repeatedly applied to the antennas over and over again, in order to provide coverage of some area of interest. Techniques borrowed from time-domain filter design such as windowing or frequency sampling can be used to determine the beamformer weights, and the primary trade-off is beamwidth/resolution versus sidelobe levels. Adaptive weight