Question

Consider an LTI channel with the response F（z）=1+0.4z⁻¹+0.3z⁻², and AWGN with a noise variance of 0.05. Consider transmitting IID symbols with a unit variance.

Design a two-tap casual ZF equalizer that enforces the equalized LTI system to have 1 and 0 as the coefficients at time 0 and 1.

Answer 1

To design a two-tap casual ZF equalizer with specific coefficients, the LTI channel response and AWGN noise variance must be considered. The ZF equalizer minimizes the mean square error and nullifies interference from the LTI channel.

Step-by-step explanation:

In order to design a two-tap casual ZF equalizer that enforces the equalized LTI system to have 1 and 0 as the coefficients at time 0 and 1, we need to consider the LTI channel response and the AWGN with a noise variance. We can start by solving for the equalizer coefficients that minimize the mean square error between the desired output and the equalized output. The ZF equalizer is designed to nullify the interference caused by the LTI channel, resulting in equalized symbols at the receiver.