Find the pre-equalizer weights g1 g2 gpsi using the zero

Question

Problem 1:

Find the pre-equalizer weights g(1), g(2), ....,g(ψ) using the zero forcing equalization principle.Problem 2:

Consider a time-invariant channel with channel response as

wheren(k) is zero-mean white Gaussian noise and the random input u(k)=+1 or -1 (BPSK) for every k. Number of channel coefficients F=5. But the channel coefficients h₁, h₂, h₃, h₄, and h₅ are unknowns.  Prof. Lu have transmitted 1100bits of u(k) through the unknown channel to each of you. What you have received is v(k) which is recorded in a file named output13.

In other words, each of you have to download output13 to obtain the data sequence v(k). The first 100 bits of the transmitted u(k), recorded in the file named training, are also known to you.

(Hint: In matlab program, use

load output13              % to get v(k)

load training                %to get u(k), k=1,2,...,100

1. You are required to, at first, find the channel vector h=[ h₁, h₂, h₃, h₄, h₅ ],

2. Secondly, design an equalizer (using two different methods)

3. Thirdly, detect the 1000 unknown u(k); k=101:1100.