How to code for maximum likelihood detector in MATLAB ?

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.

[chaaru datta]

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]

Can we say that MATLAB cant solve equation (1)....