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between two consecutive signal bursts. This is reasonable, since a mobile user in real time does not move far during one frame of observation. Hence, the variation in DOA is gradual. The approach to user tracking is based on recursive formulation for tracking DOAs where small changes in the difference of correlation matrix estimates result in small changes in difference of steering matrices through which the DOAs are extracted. One of the problems that these algorithms pose is the data association problem, that is, association of DOA estimates established at the previous time instant with that of current time instant. To overcome this problem, algorithms like constrained steepest descent (CSD), steepest descent (SD), and conjugate gradient (CD) are developed and employed [7, 8].
•Weight generation: The tracked DOA with the strongest instantaneous power is selected and thus weights for the beamforming unit to adaptively focus the beams at a desired source can be generated. Adaptive antenna algorithms like least mean square (LMS) or sample matrix inversion (SMI) [9] are used to generate these weights. The choice of the adaptive algorithm for deriving the adaptive weights is highly important in that it determines both the speed of convergence and hardware complexity required to implement the algorithm.
1.2Overview of This Book
DOA estimation algorithms form the heart of smart antenna systems. Across the board, there are a variety of DOA estimation algorithms for use in smart antenna systems targeted at position-location applications [10], and more are emerging [3, 11]. The challenge for a designer, however, is to choose the right DOA estimation algorithm because the most advanced smart antenna implementations involve simultaneously maximizing the useful signal and nulling out the interference sources. Even with the powerful signal processing units available today, it is a challenging task to perform this in real time. Consequently, efficiency and effectiveness of an algorithm become critical in selecting a DOA estimation algorithm. In other words, a thorough understanding of a DOA estimation algorithm is needed for a designer who will use the smart antenna technique.
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This book is intended to provide an introduction to the basic concepts of DOA estimations with an overview of basic techniques. In addition, the algorithms that belong to the family of ESPRIT (estimation of signal parameters via rotational invariance techniques) will be elaborated in more detail. This is because of ESPRIT’s simplicity and high-resolu- tion capability as a signal subspace-based DOA estimation algorithm; based on it, many state-of-the-art techniques have been developed.
Currently, few books are available commercially that systematically describe the principles and basic techniques of DOA estimations. This book is intended to add to that knowledge base by providing an overview and a performance analysis of the basic DOA algorithms and comparisons among themselves. In particular, systematic study, performance analysis, and comparisons of the DOA algorithms belonging to the family of ESPRIT are provided. In short, this book lays out the theoretical foundations of DOA estimation techniques for a reader to understand DOA basics and to continue on to advanced DOA topics if he or she wishes [10, 11].
The book is aimed at beginners such as graduate students or engineers or government regulators who need to gain rapid insight into the fundamentals of DOA estimations. It is also suitable for those who specialize in the area but would like to refresh their knowledge of the basics of DOA estimations.
1.3 Notations
In this work, vectors and matrices are denoted in bold letters, either lowercase or uppercase. The superscripts ( )H and ( )T denote complex conjugate transposition and transposition without complex conjugation, respectively. The overbar () denotes complex conjugate. E{ } denotes
expectation operator. Rm×n refers to a real number matrix of m rows and n columns. Cm×n refers to a complex number matrix of m rows and n columns. means belong to. Frequently used exchange matrix Πp and diagonal matrix are briefly explained in the appendix. Also, a definition of Kronecker products is provided in the appendix.
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References
[1]Federal Communications Commission, http://www.fcc.gov/e911/.
[2]Liberti, Jr., J. C., and T. S. Rappaport, Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications, Upper Saddle River, NJ: Prentice-Hall, 1999.
[3]Sarkar, T. K. Smart Antennas, New York: IEEE Press/Wiley-Interscience, 2003.
[4]Kuchar, A., et al., “A Robust DOA-Based Smart Antenna Processor for GSM Base Stations,” Proc. IEEE Intl. Conf. on Communications, Vol. 1, June 6–10, 1999, pp. 11–16.
[5]Balanis, C. A., Antenna Theory: Analysis and Design, 3rd ed., New York: Wiley, 2005.
[6]Hallen, A. D., and C. Heegard, “Delayed Decision Feedback Sequence Estimation,” IEEE Trans. on Communications, Vol. 37, No. 5, May 1989, pp. 428–436.
[7]Griffiths, L. J., and C. W. Jim, “An Alternative Approach to Linearly Constrained Beamforming,” IEEE Trans. on Antennas and Propagation, Vol. AP-30, No. 1, January 1982, pp. 27–34.
[8]Karttunen, P., and R. Baghaie, “Conjugate Gradient Based Signal Subspace Mobile User Tracking,” Proc. IEEE Vehicular Technology Conference, Vol. 2, May 16–20, 1999, pp. 1172–1176.
[9]Compton, Jr., R. T., Adaptive Antennas, Englewood Cliffs, NJ: Prentice-Hall, 1988.
[10]Krim, H., and M. Viberg, “Two Decades of Array Signal Processing Research,” IEEE Signal Processing Magazine, Vol. 13, No. 4, July 1996, pp. 67–94.
[11]Van Tree, H. L., Optimum Array Processing, New York: John Wiley & Sons.
2
Antennas and Array Receiving System
An antenna is basically a transducer designed to transmit or receive electromagnetic waves or radio signals that propagate in air or in a medium [1]. A transmit antenna takes in currents out of electronic devices and transforms them into the corresponding electromagnetic or radio signals that radiate into air or a medium. A receive antenna does the opposite: it captures or intercepts electromagnetic waves or radio signals in the air or a medium and then transforms them into corresponding currents and sends them to the connected electronic devices. In short, an antenna serves as an interfacing device between air (or a medium) and electronic devices, making possible the realization of a wireless system as shown in Figure 2.1. They are often seen and used in systems such as radio broadcasting, radio communications, cellular phone systems, wireless local area networks (LAN), radar, and space exploration. Without antennas, there would be no modern wireless communications and telemetry industry.
Physically, an antenna is an arrangement of conductors and surrounding materials that will either generate radiating electromagnetic waves in response to currents or voltages applied to the antennas or induce currents and voltages in it due to electromagnetic waves or radio signals impinging on it. Different ways of the arrangements or positioning of the conductors and materials lead to various antennas with different behaviors and properties. Figure 2.2 shows a monopole antenna
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Introduction to Direction-of-Arrival Estimation |
Figure 2.1 Wireless transmission via antennas.
Figure 2.2 A monopole antenna mounted on a car and a microstrip patch antenna.
mounted on a car for receiving radio broadcasting and a microstrip patch antenna seen in some cellular phones or wireless USBs.
In theory, both transmit and receive antennas need to be studied separately because of their different functions. Fortunately, it has been found that transmit and receive functions of an antenna are reciprocal. Therefore, in most literature so far, only transmission properties of an antenna are studied and analyzed; when an antenna is used for receiving, its receiving properties are simply extracted from its transmitting properties through the reciprocity.
Various antenna parameters have been introduced to quantify the performance of an antenna. In this chapter, we will describe the important parameters and concepts that are pertinent to the DOA estimations.