Assume that the channel transfer function is uiwith u101 u01

Assume that the channel transfer function is u(i)with u(-1)=-0.1, u(0)=1, u(1)=0.2. Design a 3-tap ZF equalizer to force the impulse response to be 0 for i=-1, 1 and 1 for i=0. What are the weights of the equalizer? (Notice that [1 -0.1 0; 0.2 1 -0.1; 0 0.2 1]^(-1) = [0.9808 0.0962 0.0096; -0.1923 0.9615 0.0962; 0.0385 -0.1923 0.9898]) 0.0962, 0.9615, -0.1923. 0.9808, -0.1923, 0.0385 0.0096, 0.0962, 0.9808 0.9808, 0.9615, 0.9808

Solution

[C-1; C0 ;C1] = [0.9808 0.0962 0.0096; -0.1923 0.9615 0.0962; 0.0385 -0.1923 0.9898] [0 ; 1; 0]

C-1 = 0.0962

C0 = 0.9615

C1= -0.1923