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How to code the following expression in MATLAB

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chaaru datta
chaaru datta el 22 de Oct. de 2023
Comentada: chaaru datta el 25 de Oct. de 2023
Hello all, I am trying to understand how to code the following equation (1) in MATLAB: ----(1)
where,
, such that each of is a column vector of dimension 8 X 1, L denotes total time slots.
And each is drawn randomly from set .
Also i.e., denotes cardinality of a set.
If N = 16 and if are as follows:
x_1 = [xs xs 0 0 0 0 0 0 ]'; x_2 = [xs 0 xs 0 0 0 0 0 ]'; x_3 = [xs 0 0 xs 0 0 0 0 ]'; x_4 = [xs 0 0 0 xs 0 0 0 ]';
x_5 = [xs 0 0 0 0 xs 0 0 ]'; x_6 = [xs 0 0 0 0 0 xs 0 ]'; x_7 = [xs 0 0 0 0 0 0 xs ]'; x_8 = [0 xs xs 0 0 0 0 0 ]';
x_9 = [0 xs 0 xs 0 0 0 0 ]'; x_10 = [0 xs 0 0 xs 0 0 0 ]'; x_11 = [0 xs 0 0 0 xs 0 0 ]'; x_12 = [0 xs 0 0 0 0 xs 0 ]';
x_13 = [0 xs 0 0 0 0 0 xs]'; x_14 = [0 0 xs xs 0 0 0 0]'; x_15 = [0 0 xs 0 xs 0 0 0]'; x_16 = [0 0 xs 0 0 xs 0 0]';
where xs = sqrt(1/2)*(randn(1,1)+1i*randn(1,1)); % transmitted signal of Complex Gaussian nature
Any help in this regard will be highly appreciated.
  2 comentarios
chaaru datta
chaaru datta el 22 de Oct. de 2023
Any logic will help to code it more effectively.
chaaru datta
chaaru datta el 23 de Oct. de 2023
Can we say that MATLAB cannot solve such expressions....

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Respuestas (1)

Image Analyst
Image Analyst el 23 de Oct. de 2023
To get L random columns from xgssk, you can use randperm
randomColumns = randperm(size(xgssk, 2), L);
X = xgssk(1:8, randomColumns); % 8 by L matrix
You can get a random index and value from column vector xi also using randperm
index = randperm(numel(xi), 1);
value = xi(index);
  5 comentarios
Image Analyst
Image Analyst el 23 de Oct. de 2023
It says the cardinality is N^L or 16^8 = 4294967296
chaaru datta
chaaru datta el 25 de Oct. de 2023
@Image Analyst In my case L is not 8 but its value is 500....so cardinality should be 16^500.

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