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How to code for maximum likelihood detector in MATLAB ?

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chaaru datta
chaaru datta el 23 de Oct. de 2023
Comentada: chaaru datta el 23 de Oct. de 2023
Hello all, I am trying to code the following Maximum Likelihood detector expression (1) from a research paper in MATLAB.
----(1)
where denotes Frobenius norm, is the transmitted signal sequence with length L and of represents the transmitted
signal column vector of dimension 8 X 1 at the time slot and i ranges from 1 to L. Each is drawn from set , such that is channel between transmitter and receiver, is noise at receiver and is received signal.
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.
I had obtained the values of as follows:
H = sqrt(1/2)*(randn(N_r,N_t)+1i*randn(N_r,N_t)); % channel between transmitter and receiver
Noise = sqrt(1/2)*(randn(N_r,1)+1i*randn(N_r,1)); % Noise at receiver
My query is that how can we obtain and hence how can we solve equation (1) in MATLAB.
Any help in this regard will be highly appreciated.
  2 comentarios
chaaru datta
chaaru datta el 23 de Oct. de 2023
I had obtained the as follows in MATLAB.
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
chaaru datta el 23 de Oct. de 2023
Can we say that MATLAB cant solve equation (1)....

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