numerical example in matlab.

Please, I need to know numerical values can be given to the variables in this formula so that I can convert them into code.

Can you give me a numerical example please.

= + ∑1_(j=1, j≠i)^K +

where 𝑯_𝒊𝒊 and 𝑯_𝒊𝒋 the channel matrix between 𝑩𝑺𝒊 and 𝑪𝑼𝑬𝒊, CUEj (i, j ∈ {1, 2, . . . , K} , 𝑖≠𝑗.

𝑽𝒊 of dimension 𝑀 × 𝑑𝑖 and 𝑉𝑗 of dimension 𝑀 × 𝑑𝑗 are 𝑩𝑺𝒊 and 𝑩𝑺𝒋 respectively,

si with dimension di × 1 is the downlink data signal vector BSi

𝑛_𝑖 is additive white Gaussian noise.

this is an Inter-cell interference model and is the signal received by user i

Answer 1

[Eswaramoorthy]

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.