In digital communications, a considerable effort has been devoted to neutralise the effect of channels (i.e., the combination of transmit filters, media and receive filters) in transmission systems, so that the available channel bandwidth is utilised efficiently. The objective of channel neutralisation is to design a system that accommodates the highest possible rate of data transmission, subject to a specified reliability, which is usually measured in terms of the error rate or average probability of symbol error. An equaliser normally performs neutralisation of any disturbances the channel may introduce by making the overall frequency response function T(z) to be flat. Since a channel is time varying, due to variations in a transmission medium, the received signal is nonstationary. Therefore, an adaptive equaliser is utilised to provide control over the time response of a channel. Since an adaptive equaliser is an inverse system of a channel, it amplifies the frequency of noise outside the bandwidth of a channel. In order to reduce the effect of noise, a low pass filter is cascaded with the equaliser. However, the cascaded filter can introduce a negative impact on the speed of adaptation. Therefore, the bandwidth of the cascaded filter is chosen to be very wide at the beginning of the adaptation process. This way, the output reaching the static value will not be delayed. As the output of the adaptive filter is close to the static value, the bandwidth decreases to cancel the effect of noise. The adaptive rule for noise filter can be defined as (I). The constants alpha and beta depend on the level of noise and are chosen by trial and error method. Delta is a variable that is used to change the value of tau and consequently the bandwidth of the filter. Delta acts as an input to the proportional controller. Furthermore, in the same equation, beta represents a proportional (P) controller gain (Kp). In order to reduce the disturbance rejection bandwidth, improve speed.
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