How to code the following expression in MATLAB
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Hello all, I am trying to understand how to code the following equation (1) in MATLAB: 
----(1)
----(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 
.
is drawn randomly from set .Also 
i.e., 
denotes cardinality of a set.
i.e., denotes cardinality of a set.If N = 16 and if 
are as follows:
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.
Answers (1)
Image Analyst
on 23 Oct 2023
5 Comments
chaaru datta
on 23 Oct 2023
Thank u so much sir for your response....
I am not getting how cardinality of set is 
and how to implement it in MATLAB.
and how to implement it in MATLAB.I think by x[1] it means your x_1 column vector, and x[2] is really x_2 so you construct xgssk like
xs = sqrt(1/2)*(randn(1,1)+1i*randn(1,1)); % transmitted signal of Complex Gaussian nature
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]';
xgssk = [x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11, x_12, x_13, x_14, x_15, x_16]
chaaru datta
on 23 Oct 2023
@Image Analyst Thank u sir....I had also prepared the 
in the same way...but the problem is that I am not getting what cardinality has to do with it...I mean I am nowhere finding the 
....
in the same way...but the problem is that I am not getting what cardinality has to do with it...I mean I am nowhere finding the ....
Image Analyst
on 23 Oct 2023
It says the cardinality is N^L or 16^8 = 4294967296
chaaru datta
on 25 Oct 2023
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