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.

2.1 Single Transmit Antenna

It has been found and proven that the following properties exist for a transmit antenna:

1.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.

2.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.

2.1.1Directivity and Gain

These two parameters basically quantify how well an antenna can concentrate its radiated energy in a specific direction. 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 2.3.

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

Figure 2.3 The omnidirectional antenna and its radiation distribution.

reference antenna (the omnidirectional isotropic antenna) in a given direction at an arbitrary distance. 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.

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 2.4). The efficiency is less than or equal to 100%. As a result, the gain is less than or equal to the directivity.

2.1.2Radiation Pattern

Radiation pattern of an antenna is the geometric pattern of the relative strengths of the field emitted by the antenna in respect to the radiation directions. For the ideal isotropic omnidirectional antenna, this would be a sphere, meaning that the radiation intensity generated is the same in every direction. For a typical dipole, however, this would be a toroid or “donut.” Figure 2.5 shows the patterns of two antennas, a dipole and a waveguide horn. In the radiation pattern, the longer radius of the pattern represents the stronger radiation intensity. By examining a radiation

Figure 2.4 Power relationship in a transmit antenna.

Figure 2.5 Radiation patterns of a dipole and a waveguide horn (open-ended waveguide).

pattern of an antenna, we are able to see in which direction an antenna radiates the most and in which direction the least.

2.1.3Equivalent Resonant Circuits and Bandwidth

Like many field-based devices, an antenna can be made equivalent to a resonant circuit in terms of its input terminal voltage and current, as shown in Figure 2.6. 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 fre- quency-selective nature of an antenna. The input signals of the frequencies near the resonant frequency of the antenna can easily go in the