Here is a numerical example. Let's say we have the following values:
- K = 3 (i.e., there are three CUEs)
- M = 4 (i.e., the dimension of the transmitted signal is 4)
- d1 = 2, d2 = 3, d3 = 2 (i.e., the dimensions of the received signal for each CUE are 2, 3, and 2, respectively)
- 𝐻_𝑖𝑗 = [1.2 -0.3; 0.7 0.8] for all i ≠ j (i.e., the channel matrix between BS i and CUE j is a 2x2 matrix with specific values)
- 𝑉_𝑖 = [0.9 0.2 0.1 -0.1; -0.5 0.6 0.3 -0.2] for all i (i.e., the matrix representing the transmitted signal from BS i is a 2x4 matrix with specific values)
- 𝑆_𝑖 = [1; 2] for all i (i.e., the downlink data signal vector for each BS is a 2x1 vector with specific values)
- 𝑛_𝑖 ~ N(0, σ^2) for all i (i.e., the noise term for each CUE is a Gaussian random variable with mean 0 and variance σ^2)
Then, we can calculate the received signal for each CUE using the formula you provided:
𝑦_𝑖 = 𝐻_𝑖𝑖 𝑉_𝑖 𝑆_𝑖 + ∑_(j=1,j≠i)^K 𝐻_𝑖𝑗 𝑉_𝑗 𝑆_𝑗 + 𝑛_𝑖
For example, if we want to calculate the received signal for CUE 1, we can plug in the values:
𝑦_1 = [1.2 -0.3; 0.7 0.8] [0.9 0.2 0.1 -0.1; -0.5 0.6 0.3 -0.2] [1; 2] + [1.1; -0.3]
This will give us a 2x1 vector representing the received signal for CUE 1. We can repeat this process for CUE 2 and CUE 3 to get the received signals for all CUEs.
