In this section we explain what a channel is and present its common effects on the transmission session. We conclude with few examples for classic channels and briefly present methods to overcome their effect.
The channel is actually a mathematical model that represents physical phenomena. The input of the channel is an analog signal and so is its output. The channel's mathematical model, or simply "the channel", is based on the deployed transmission media and environmental condition. For example, an optic fiber and a coaxial cable have different behaviors and traits, so we have to model them differently. Another example: due to an electromagnetic flux caused by a lightening storm, we might need to change our model since the older model no longer reflects the physical conditions.
Though the environment is chaotic and highly unstable, we simplify matters by assuming that the channel does not change its behavior rapidly. This assumption offers schemes for both the transmitter and the receiver to adapt to these changes, so we can say that the channel is well known to both sides and we may assume that it does not change its characteristics throughout the entire communication session.
A typical way to model a physical channel is to divide its effects into two categories. The first is the channel's deterministic influence. This category might include effects such as attenuation (which is very common throughout wires) and inter-symbol interference (ISI). When the transmitted signal gets to the receiver through different routes, the receiver gets replicas of the signal in various times. The receiver, in turn, might confuse and relate the delayed signals to the next transmitted session. This phenomenon is called ISI. The second category is the channel's stochastic influence. This category models our "uncertainty" due to the chaotic behavior of nature. For instance, the electrons located throughout a cable roam in random direction and speed.
We start by reviewing the simplest channel and gradually generalize the model. We denote the original signal by S(t) and the received signal by R(t), noise will be denoted by N(t).
In this model the channel has only stochastic influence. In most cases, the stochastic influence is actually an interference simply called noise. It is caused by enormous number of tiny interference.For instance small electrons that roam disorderly through the media and "bump into" our signal's electron. The Central Limit Theorem advocates that the general total interference has a Gaussian distribution. Moreover, we assume that this distribution is the same at every time and does not depend on its past. In this case, the stochastic process is said to be white. Continuing with our previous example, the electrons "bump into" each other so there is no guarantee that the electrons stay in their original course or even reserve their speed, so we can't predict what will happen in a short while.
Fortunately, modems were introduced to deal with such channels.
This model extends the AWGN model simply by assuming that the stochastic process is not white, meaning that the noise distribution in this very moment might depend on its past behavior. This model is very popular when the channel's past behavior influence the channel's present one. Consider the previous example for instance, but now assume that when electrons "bump into" the signal's electrons (which have common direction and speed) the cable gets heated, resulting in more vigorous electron movement and so on.
Under some assumption about the noise spectrum's regularity, we can design a filter (and put it at the receiver's side) which transforms the colorful noise into a white noise. This filter is called a whitening filter. Note that in this situation we have to carefully design the constellation so that the result after the whitening filter will be as our desired constellation.
This Model extends the AWGN model simply by assuming that the channel has a deterministic effect. We assume that the effect can be modeled as an LTI system that might cause ISI. For example, think about a cell-phone that transmits directly to the cell-phone operator, but also transmits the same signal to an obstacle, say a building, which reflects the (possibly attenuated) signal back to the cell-phone operator. The result is ISI.
Fortunately enough, we know several schemes for ISI elimination. For instance, by putting an equalizer at the receiver's side the ISI effects can be approximately eliminated. In fact, the equalizer is a component whose purpose is to eliminate the ISI effects by using estimation methods.
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