It is also suitable for those who specialize in the area but would like to refresh their knowledge of the basics of DOA estimations. The overbar denotes complex conjugate. C refers to a complex number matrix of m rows and n columns. Also, a definition of Kronecker products is provided in the appendix. IEEE Intl. AP, No.
Table of contents
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. 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. 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. Antennas and Array Receiving System 23 We will first discuss a single transmit antenna, a single receive antenna, and then antenna arrays that consist of many single antennas and are used for DOA estimations.
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The electromagnetic energy radiated out of an antenna is often not uniformly distributed in space. Radiation intensity is normally stronger in one direction than in other directions. Not all the frequencies of radio signals are radiated effectively out of an antenna. Some frequencies are transmitted into air or a medium very efficiently and others not at all.
To describe these two phenomena, the following parameters have been introduced for an antenna: 1. Directivity and gain that describe the degree of energy concentration in a direction by an antenna; 2. Radiation pattern that shows the relative radiation intensities in all the directions; 3. Equivalent resonant circuit and bandwidth that shows how an antenna behaves in terms of frequency responses.
To quantify, a reference antenna needs to be taken. In most cases, an omnidirectional antenna that radiates equally in all directions is taken as the reference antenna as shown in Figure 2. The directivity of an antenna is then defined as the ratio of the radiated power intensity of an antenna in one direction to that of the omnidirectional antenna in the same direction when both antennas radiate the same total power. In other words, the directivity of an antenna measures the amount of power intensity by an antenna over that by the 24 Introduction to Direction-of-Arrival Estimation Figure 2.
If the directivity is unity in all the direction, the antenna is an omnidirectional antenna. Strictly speaking, the directivity of an antenna depends on the directions at which the radiation intensity is measured and compared with that of the reference antenna. However, in a normal circumstance, the term directivity refers to the maximum directivity among all the directions by an antenna.
Introduction to Direction-of-Arrival Estimation (Artech House Signal Processing Library)
The gain of an antenna is directly related to its directivity. The gain is equal to the product of the directivity and the antenna efficiency. The efficiency accounts for internal power ohmic loss of the antenna; it is equal to the ratio of the total power radiated into air or a medium by an antenna to the power input to the antenna by the electronic device connected to the antenna see Figure 2. As a result, the gain is less than or equal to the directivity.
For the ideal isotropic omnidirectional antenna, this would be a sphere, meaning that the radiation intensity generated is the same in every direction. In the radiation pattern, the longer radius of the pattern represents the stronger radiation intensity. In the circuit, in addition to a resistor that represents the internal ohmic power loss of an antenna, there is another resistor called a radiation resistor that describes the amount of power radiated into air or a medium.
The inductor and capacitor represent the frequency-selective nature of an antenna. The input signals of the frequencies near the resonant frequency of the antenna can easily go in the 26 Introduction to Direction-of-Arrival Estimation Figure 2. A typical relationship between the input power and the frequency is shown in Figure 2.
Like the bandwidth definition for a resonant circuit, the difference between the two frequency points at which the power drops to the half of its maximum is defined as the bandwidth of an antenna. Within the bandwidth, we consider that the degree of the power radiation is acceptable. Theoretically, a receive antenna should also have its own parameters that quantify its performance. Antennas and Array Receiving System 27 pattern that describe how a receive antenna captures different energy amounts of electromagnetic or radio signals coming from different directions in reference to an omnidirectional receive antenna.
However, it has been found and can be proven that these parameters have the same values or shape as the transmit directivity, gain, and pattern when the same antenna is used as a transmit antenna. As a result, in almost all the antenna analysis, directivity, gain, and radiation pattern are referred to those when an antenna is used for transmission. In other words, when an antenna is to be used for receiving, its receive parameters are simply taken from those transmit parameters when the antenna is analyzed for transmission; the exception is, however, the equivalent circuit.
The equivalent circuit of a receive antenna is shown in Figure 2.
It is exactly the same as the equivalent circuit of the antenna when it is used for transmission, except a voltage or current source is added. The current source represents the equivalent current induced by the presence of the electromagnetic fields near the receive antenna. The resistances, inductance, and capacitance remain the same as those of the transmit antenna. Each individual antenna is often called an array element. For a receive array, the signals received by all array elements will be combined and then processed for various applications, including the DOA estimations.
For illustration purposes, let us consider a three-element that is aligned uniformly along a line as shown in Figure 2.
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The other two elements are numbered as element 2 and element 3 in a sequence from right to left. A source emits electromagnetic waves at such a far distance that the three propagation line paths from the source to the three elements can be approximately considered as parallel. Equation 2.
In short, an antenna is a transducer device that interfaces electronic devices with air or a medium for the purpose of 30 Introduction to Direction-of-Arrival Estimation transmitting or receiving electromagnetic waves or radio signals. Due to the fact that an antenna radiates its energy nonuniformly in space, parameters such as directivity, gain, and radiation pattern are often used to quantify performances of an antenna.
Since an antenna is also frequency-selective, an equivalent circuit can be introduced to describe an antenna in terms of its terminal voltage and current.
About this book
Because of the reciprocity of transmit and receive operations of an antenna, the performances of an antenna are often investigated for its transmit properties; the results can be directly used for an assessment of its receive performance. There is a huge body of published literature on various topics of antennas. Such a large amount of available information usually gets a nonantenna specialist lost or confused in selecting a good text as a starting point. In order to avoid the similar confusion, we list only a single reference in this chapter.
This reference is the excellent textbook by C. Balanis ; it presents an introduction to various topics of antenna technologies including the basic concepts of antennas and arrays; the contents of the book are very much sufficient for the potential readers of this book. Reference  Balanis, C. In general, the direction-of-arrival DOA estimation techniques can be broadly classified into conventional beamforming techniques, subspace-based techniques, and maximum likelihood techniques.
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This chapter is organized as follows. In Section 3. A uniform linear array is used to explain this model. Later, the basic principles of a few basic algorithms belonging to each DOA class are briefly discussed. An excellent doctoral dissertation on array signal processing for DOA estimations by M.
Haardt was published by Shaker Verlag . This book uses it as one of the major references. In order to facilitate a reader in checking on this major reference without much confusion, this book employs the same mathematical symbols and technical terms as those in ; these symbols and terms have also been used in other related literature.
The prevailing data model used in the remainder of this book is discussed in this section. The transmission medium between the sources and the array is assumed to be isotropic and linear; in other words, the medium has its physical properties the same in all different directions and the signals or waves at any particular point can be superposed linearly.
The isotropic and linear property of the medium ensures: 1 that the propagation property of the waves do not change with the DOAs of signals, and 2 that the signals traveling through the medium and then impinging on or received by any element of the M-element array can be computed as a linear superposition of d signal wavefronts generated by the d sources. In addition, the gain of each antenna or sensor element is assumed to be one. Thus, the propagating fields of the d signals arrived at the array are considered as parallel to each other.
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This assumption can, in general, be realized by making the distance between the signal sources and the array much larger than the dimension of the antenna array. The additive noise is taken from a zero mean, spatially uncorrelated random process, which is uncorrelated with the signals. Figure 3.