The Channel

The channel is the medium through which we transmit information. There are essentially two types of channels. The "wired" channel consists of media such as copper wire, co-axial cables, and fiber optic cables. The "wireless" channel consists of media such as air, water, vacuum, or earth.

Lab 8 transmitted information through a copper "wired" channel. In this case, we simply applied a voltage at one end of the wire. The receiver at the other end of the wire would detect the potential drop. In a wireless channel, information propagation is more complex. In most cases, wireless channels rely on wave dynamics to transmit energy through the medium. As an example, we might consider a channel such as the atmosphere and the propagation of light across this channel. Light is an electro-magnetic (EM) wave. Essentially, this means that we have electrical and magnetic fields that pass energy back and forth between each other. The dynamics of this interaction are such that the wave propagates over a distance. Other wireless channels supporting either acoustic (air/water) or seismic (earth) waves rely on similar dynamical mechanisms for wave propagation

A channel is not an ideal medium for energy transmission. Channels often distort the signals that pass through them. The channel can add "noise" to the signal. In particular, we can think of the channel (such as the atmosphere) as a "system block". The input into the block is the transmitter's output signal and the output of the channel is then input into the receiver. If the channel can be represented as a linear system, then we may relate the channel's input $x(t)$ to its output, $y(t)$, through the following equation

$$Y(s) = H(s) X(s) + N(s)$$ (1)

where $X(s)$ and $Y(s)$ are the Laplace transforms of the input and output, respectively. $H(s)$, of course, is the transfer function for the channel and $N(s)$ is an additive noise term.

Recall from the last chapter that $\vert H(j \omega)\vert$ is network's frequency response. So, for instance, we could graph the spectrum of a wireless channel as a function of the frequency of the EM wave that's propagating over the channel. One possible frequency response is shown below in figure 3. What you'll see is that the atmospheric channel's transfer function has several "holes" in it. The holes refer to places where the atmosphere absorbs EM radiation. Obviously, if we were to transmit a signal in a frequency range covered by one of these holes, then very little of the signal would reach the receiver. So the transmitter usually encodes the information signal onto a carrier wave whose frequency sits in one of the frequency "windows" in which the atmosphere is nearly transparent. One of these particular windows occurs in the infra-red (IR) range of the EM spectrum, which is why we're building an IR wireless link in this lab.

Figure 3: Atmospheric Channel's Frequency Response