Intersymbol interference

The symbol crosstalk, also known as inter-symbol interference (ISI), with digitally coded transmission techniques describes interference between successive transmit symbols. In contrast to the cross-talk, which describes a mutual cross-talk spatially adjacent transmission paths and also analog broadcasts may concern, the symbol relates to a crosstalk of the same transmission channel, the temporal sequence of symbols used for the digital transmission.

Causes

In digital transmission, the discrete-value information in a time- consecutive symbols is transmitted over a channel. This channel may for example be a radio link or a wired transmission. Icon crosstalk is this caused by the following reasons:

Band-Limited Channels

Since each transmission channel has a bandwidth limitation and secondly a transmission channel to be used as efficiently as possible, there are certain boundary conditions, under which, for a given bandwidth ISI - free transmission is still possible. These are summarized in the two Nyquistbedingungen which must be met for the avoidance of -symbol interference due to band limiting.

First Nyquist

The first Nyquist criterion states that the impulse response h (t) of the entire transmission system with the sampling at the sampling instants t n × T ( n is an integer ) must satisfy the following condition:

This means that a particular transmission symbol, which is sent at time n = 0, has to be at all other sampling points zero. To satisfy this condition, so-called pulse shaping filters. One example is the raised cosine filter (RC - pulse) called, whose impulse response is shown on the right for a sequence of five transmission pulses. Each RC pulse is only accurate in its sampling 1 and to all other sampling times equal to 0, so no symbol crosstalk occurs. As another example, the ideal low-pass filter satisfies the first Nyquist criterion, but can not be implemented due to the lack of causality.

Second Nyquist

The second Nyquist represents a tightening of the first Nyquist criterion and additional requirement that the impulse response h (t ) of the filter exactly must have the value 1 /2 between two sampling instants. This circumstance can be graphically clarified in the eye diagram: the first Nyquist criterion calls for the maximum opening of the eye at the sampling time t = 0 in the vertical direction. The second Nyquist urges the maximum opening of the eye in the horizontal direction of the symbol duration T.

In the adjacent eye diagram the second Nyquist is just not satisfied. The RC pulse of a raised cosine filter fulfills the Nyquist criterion for the second so-called roll-off factor of β = 1. In this case, the signal edge of the RC pulse is a Nyquist slope dar.

In many practical transmission systems, the second Nyquist criterion is not met exactly. The less the second Nyquist criterion is met or the farther the eye is closed in the horizontal direction, the more accurate the symbol clock at the receiver needs to be.