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One of the causes of intersymbol interference is multipath propagation in which a wireless signal from a transmitter reaches the receiver via multiple paths. The causes of this include reflection (for instance, the signal may bounce off buildings), refraction (such as through the foliage of a tree) and atmospheric effects such as atmospheric ducting and ionospheric reflection.
In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel (including responses of transmit and receive filters), result in no intersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference.
This is intended to remove the effect of channel from the received signal, in particular the intersymbol interference (ISI). The zero-forcing equalizer removes all ISI, and is ideal when the channel is noiseless.
Not every filter can be used as a pulse shaping filter. The filter itself must not introduce intersymbol interference — it needs to satisfy certain criteria. The Nyquist ISI criterion is a commonly used criterion for evaluation, because it relates the frequency spectrum of the transmitter signal to intersymbol interference.
The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simplest form (=) is a cosine function, 'raised' up to sit above the (horizontal) axis.
To have minimum ISI (Intersymbol interference), the overall response of transmit filter, channel response and receive filter has to satisfy Nyquist ISI criterion. The raised-cosine filter is the most popular filter response satisfying this criterion. Half of this filtering is done on the transmit side and half is done on the receive side.
Intersymbol interference can be avoided if the multipath time-spreading (the time between the reception of the first and the last echo) is shorter than the guard interval (i.e., 125 microseconds). This corresponds to a maximum difference of 37.5 kilometers between the lengths of the paths.
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. [1] It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading.