For most wireless communications, channels (what happens between the transmitter and receiver) are complicated things. For the sake of introduction, in this section we consider a single transmit antenna and receive antenna, residing in a universe without scatterers or blockage.

Antennas

The study and design of antennas is a rich field [15]. Here, we focus on a small set of essential features. The first important concept is that antennas do not radiate power uniformly in direction or in polarization. The radiated power as a function of direction is denoted the radiation pattern. If the antenna is small compared with the wavelength (for example, if the antenna fits easily within radius of a 1/8 wavelength), then the shape of the radiation pattern is relatively smooth. However, if the antenna is large compared with the wavelength, then the radiation pattern can be complicated. Antenna patterns are often displayed in terms of decibels relative to a notional isotropic antenna (denoted dBi). The notional isotropic antenna has the same gain over all 4π of solid angle. Gain is an indication of directional preference in the transmission and reception of power. The axisymmetric radiation pattern for an electrically small (small compared with a wavelength) dipole antenna is displayed in Figure 5.1. In the standard spherical coordinates of r, θ, φ, which correspond to the radial distance, the polar angle, and the azimuthal angle, respectively, the far-field electric field is limited to components along the direction of θ, denoted eθ.