In general wireless communication systems are modeled as linear time-invariant (LTI) systems. The received signal is considered the convolution of a transmitted signal and channel input response (CIR) in the time domain. In the frequency domain, we observe a slight frequency shift. To retrieve the original signal at the receiver side, we need to go through the 'deconvolution' process. There the no standard process named 'deconvolution' in the case of wireless communication. The equalization process does the same job.
The function of an Equalizer
The channel estimate is followed by the equalizer's operation. A signal processing procedure known as equalization decreases inter-symbol interference, or ISI. Equalization is the reversal of distortion that a signal experiences during channel transmission. Since equalization is an inverse channel filter, we can say that.
When we transmit a signal from the transmitter side, it reaches at receiver with different time delays. So, a shift frequency shift occurs. The main function of an equalizer is to estimate the original signal from known pilot bits.
with the help of an equalizer, we can calculate the channel impulse response from the received bits/symbols and training bits.