Branch : Computer Science and Engineering
Subject : Wireless Communication
Adaptive Equalization
Introduction:
Adaptive equalizers compensate for signal distortion attributed to inter symbol interference (ISI), which is caused by multipath within time-dispersive channels. Typically employed in high-speed communication systems, which do not use differential modulation schemes or frequency division multiplexing. The equalizer is the most expensive component of a data demodulator and can consume over 80% of the total computations needed to demodulate a given signal
Adaptive Equalizer:
- The basic structure of an adaptive equalizer is shown in Figure 13.8, where the subscript k is used to denote a discrete time index
- Notice in Figure 13.8 that there is a single input y_{k} at any time instant. The value of y_{k}depends upon the instantaneous state of the radio channel and the specific value of the noise (see Figure 13.1).
- The adaptive equalizer structure shown above is called a transversal filter, and in this case has N delay elements, N I taps, and N I tunable complex multipliers, called weight
- The adaptive algorithm is controlled by the error signal ek. This error signal is derived by comparing the output of the equalizer, dk. The adaptive algorithm uses Ck to minimize a cost function and updates the equalizer weights in a manner that iteratively reduces the cost function
Algorithm:
- The input signal to the equalizer as
- The output of the adaptive equalizer is a scalar given by
- Weight vector can be written as
- Output in vector notation as
- Error signal ek is given by
- Putting the value of d_{k}and d_{k}‘the error signal is