Signal-Space-Representation

Table of contents:

1. Gram-Schmidt Orthogonalization
2. Signal Space Representation
3. Signal Space Representation with adding AWGN
4. Noise Effect on Signal Space

Gram-Schmidt Orthogonalization

- Gram-Schmidt orthogonalization is a process used to transform a set of linearly independent vectors into an orthogonal or orthonormal set.

Figure 1 Φ1 VS time after using the GM_Bases function

Figure 2 Φ2 VS time after using the GM_Bases function

Signal Space Representation

Figure 3 Signal Space representation of signals s1,s2

Signal Space Representation with adding AWGN

Case 1: 10 log(E/σ^2) = 10 dB

Case 2: 10 log(E/σ^2) = 0 dB

Case 3: 10 log(E/σ^2) = -5 dB

Noise Effect on Signal Space

-As the variance (σ^2) of the additive white Gaussian noise increases, the spread of the signal points in the signal space representation also increases. The noise introduces uncertainty and randomness in the received signals, causing the signal points to scatter and deviate from their original positions. Consequently, the accuracy of the signal space representation decreases as the noise effect increases.

Contributors:

Heba Ashraf

Ahmed Lotfy