How to implement the given maximum likelihood detection equation in MATLAB ?

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charu shree 2023-3-29

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编辑： Torsten 2023-3-29

Hello all, I am trying to implement the following expression in MATLAB but not getting it properly.

where

is a L dimensional set having its cardinality as

I am having the values of

and

but I am not getting how do we proceed with

in MATLAB.

Any help in this regard will be highly appreciated.

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charu shree 2023-3-29

Thank you so much sir for your resposne.

1) Sir, X is a matrix having dimension N_t x L but its not complex in nature. In fact each column of X is a vector having 1 at only two positions and 0 every where.

2) We consider Frobenius norm for minimization.

3) Yes, Y-H*X is complex matrix.

4) H and X values are random in nature so we have to estimate them.

Torsten 2023-3-29

编辑：Torsten 2023-3-29

Define

N_t*L + 2*N_r*Nt optimization variables.

The first N_t*L variables are the X_ij defined as integer variables with the constraints

sum_i X_ij = 2 for all j , 0 <= X_ij <= 1, for 1<=j<=L

and the second 2*N_r*Nt variables are the real and imaginary parts of the H_ij = H_ij^(1) + 1i* H_ij^(2).

Then use "ga" to solve this nonlinear optimization problem.

I'm still not convinced that the H_ij are really unknown solution variables.

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