Question 6 (6 marks)
Given a 2-by-2 multiple-input multiple-output system:
The signals received at the receiver (Rx) are:
$y_1(t) = (-0.648 \quad -0.365 \quad 0.260 \quad -0.041 \quad -0.435)$
$y_2(t) = (-0.105 \quad 0.282 \quad 0.395 \quad -0.024 \quad 0.202)$
It is given that the channel coefficients are $(a, b, c, d) = (0.25, -0.62, 0.38, -0.17)$. Estimate the transmission
signals $x_1(t)$ and $x_2(t)$. Show all your calculation steps clearly.
Hint: Use the mathematical fact on matrix inverse:
$G = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \implies G^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \quad \text{if } ad - bc \ne 0.$
