A digital transmission system as shown in Figure 1 consists basically of the same components like an analog transmission system, namely a transmitter and receiver. But as shown in Figure 1, the transmission channel is also an important part of the whole system since it introduces disturbances on the signal that make the correct reception of the signal difficult, if not impossible at the receiver.

If you take for example an analog FM (german UKW) radio, it is quite well known, that the larger the distance between the transmitter and the receiver gets, the more 'noisy' the signal becomes. This can be explained by the fact, that the so-called Signal-to-Noise-Ratio (SNR) E_S/N₀ is decreasing with increasing distance. In this case, the received signal energy E_S is getting lower while the Noise N₀ = k*T_Noise is staying constant, where 'k' is the Boltzmann-constant and T_Noise is the so-called noise-temperature. To compare this effect with digital transmission systems, first a look can be taken at Figure 2, which shows a digital signal that is to be transmitted. As an example, a so-called Quarternary Phase Shift Keying (QPSK) modulation technique is used. From Figure 2 it can be seen that it consists basically of 4 different constellation points in the Inphase/Quadrature (I/Q) diagram. Of course only one signal (in this case here only one symbol) can be transmitted on one carrier at a time, but due to the high transmission speed the oscilloscope shot in Figure 2 shows several consecutive of these symbols, that seem to be connected to each other by lines. In the case of a Multi-Carrier (MC) transmission, like for example Orthogonal Frequency Division Multiplexing (OFDM), not only one QPSK symbol is transmitted on one carrier, but several of these symbols are transmitted on several carriers at the same time.

If we now come back to the SNR mentioned before, such a digital transmitted signal (that is modulated at the chosen carrier-frequency/ies) is also influenced by the statistical noise during the transmission. Such a noise in most cases can be modelled by Additive White Gaussian Noise (AWGN). This noise has a Gaussian distribution, which means that the average value is zero and the probability density is decreasing the higher the values get. (For german readers: Take a look at 10,- DM, where Gauss and his distribution are shown.) Like the name of the noise already implies, this noise is added to the signal resulting in a received signal as shown in Figure 3.

Since there are 4 different constellation symbols with QPSK, each of these symbols can cary the information of two bits, resulting in the possible sequences 00, 01, 10 and 11. If now the noise-level gets too high, the decision in the receiver in favour of  one of these possible sequences gets more and more unreliable, resulting in an increasing Bit Error Rate (BER).
But this is not the only disturbance, that might occur during the transmission. Another effect is fading. If we come back to the analog radio, a result of this effect is known as the 'red light effect'. As possibly everybody has already experienced, it might happen that during standing at a red traffic light, the signal at one point is extremely bad and when the position of the car changes just a few decimeters, might get much better. This is due to deconstructive overlaying of several reflections/echoes of the signal. The same can happen to digitally modulated signals. The resulting received signal (without additional noise that is normally always present) is shown in Figure 4.

Since we're talking about multi-carrier transmission, not only the symbol on one carrier is displayed, but all symbols on all carriers are visualized. Furthermore since the oscilloscope shot is not the result of a real received signal, but of a simulated channel, the channel simulation parameters are changed from time to time to show the different effects. In Figure 4 it can be seen that not all carriers are influenced in the same way, but that the fading (consisting of a change of the amplitude and/or the phase) on each carrier is different. This is called frequency selective fading. Furthermore if the signal in Figure 4 is compared to the transmitted signal of Figure 2, it can be seen that not only amplitudes smaller than the original amplitude occur, but also amplitudes that are larger. This implies that there's not only deconstructive, but also constructive overlaying of delayed echoes. If the distance of the transmitter to the receiver remains unchanged and no further obstacles that might block the signal transmission are introduced, the average received signal power stays constant.
The shown fading effects result from a (complex) multiplication and/or convolution in the I/Q-plane. To summarize, a (digital) transmission channel can be characterized by multiplicative and additive disturbances that depend on the distance of the receiver to the transmitter and the surrounding scenario (for example urban, rural, etc.).

Of course all the mentioned disturbances on the signal during the transmission are unwanted effects. Therefore measures have to be taken to make sure that at least a part of these effects can be eliminated in the receiver. For this reason, the transmission channel has to be estimated, so that it is possible to remove the disturbances from the received signal. This can be done by introducing so-called pilot-symbols in the transmitted signal. With these pilot-symbols, that are known to the receiver, the channel can be estimated and the received signal equalized (corrected). Such an equalized signal is shown in Figure 5. One might now expect to see some sort of the four constellation points shown in Figure 2. It can be said that it would be possible to equalize the signal in such a way and the equalization method then would be called 'zero forcing', but since the information using QPSK-modulation is contained in the phase and not the amplitude of the signal, it is not necessary to restore the amplitude as well. On the other hand, by leaving the amplitude unchanged it is possible to obtain information about the reliability of the equalized symbol and thus making further decoding steps to decrease the BER more powerfull.