6.3 Wireless channels

Wireless channels exploit the prediction made by Maxwell's equation that electromagnetic fields propagate in free spacelike light. When a voltage is applied to an antenna, it creates an electromagnetic field that propagates in all directions(although antenna geometry affects how much power flows in any given direction) that induces electric currents in thereceiver's antenna. Antenna geometry determines how energetic a field a voltage of a given frequency creates. In general terms,the dominant factor is the relation of the antenna's size to the field's wavelength. The fundamental equation relating frequencyand wavelength for a propagating wave is $$\lambda f=c$$ Thus, wavelength and frequency are inversely related: High frequency corresponds to small wavelengths. For example, a1 MHz electromagnetic field has a wavelength of 300 m. Antennas having a size or distance from the ground comparable tothe wavelength radiate fields most efficiently. Consequently, the lower the frequency the bigger the antenna must be. Becausemost information signals are baseband signals, having spectral energy at low frequencies, they must be modulated to higherfrequencies to be transmitted over wireless channels.

For most antenna-based wireless systems, how the signal diminishes as the receiver moves further from the transmitterderives by considering how radiated power changes with distance from the transmitting antenna. An antenna radiates a givenamount of power into free space, and ideally this power propagates without loss in all directions. Considering a spherecentered at the transmitter, the total power, which is found by integrating the radiated power over the surface of the sphere,must be constant regardless of the sphere's radius. This requirement results from the conservation of energy. Thus, if $p(d)$ represents the power integrated with respect to direction at a distance $d$ from the antenna, the total power will be $p(d)\times 4\pi d^2$ . For this quantity to be a constant, we must have $$\propto (p(d), \frac{1}{d^2})$$ which means that the received signal amplitude $A_R$ must be proportional to the transmitter's amplitude $A_T$ and inversely related to distance from the transmitter.

The speed of propagation is governed by the dielectric constant ${\mu }_0$ and magnetic permeability ${\epsilon }_0$ of free space.