How to implement the given equation in MATLAB?

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chaaru datta
chaaru datta 2022-5-10
评论： chaaru datta 2022-5-13
I am studying the following equation:
here is vector of QPSK symbols, belongs to , is a random complex number, is vector and n ranges from 1 to N. Also note that I have all these values.
My query is how to implement this equation (1) in MATLAB.
Any help in this regard will be highly appreciated.
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Sam Chak
Sam Chak 2022-5-10
编辑：Sam Chak 2022-5-10
Hi @chaaru datta
It is important to understand that is NOT an equation. It is more like a problem to be solved.
Mathematically, it implies the value of x for which attains its minimum.
In your case, you should find the solution that is in the set of values .
I understand that this kind of problem can be difficult to understand for people who are not familiar with the math notations. I took a long time to get familiar with them because I don't have a Math Degree and they are often found in academic journal papers involving mathematical optimization problems.
Would suggest you to type out the values of all paramaters.
Not many people understand that QPSK stands for Quadrature Phase Shift Keying.
chaaru datta
chaaru datta 2022-5-12
Thank you so much sir for your reply..... I am sharing the values of all parameters by assuming n to be ranging from 1 to 8.
.

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Sam Chak
Sam Chak 2022-5-12
Thanks @chaaru datta. But the data you shared are non-copyable because they are images.
You can click the MATLAB code button and dump the data there.
Anyhow, you can try this simple method to find the value that gives the minimum. I copied only 3 sets of data pairs only, but you should get the idea how to do it.
Psi = -0.06-1.16i;
ym = [-0.41+0.41i 0.54-0.58i -0.62-0.71i]
sm = [0.70+0.70i -0.70-0.70i -0.70+0.70i]
fcn = (abs(Psi*ym - sm)).^2
[fmin, idx] = min(fcn)
sm(idx)
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Sam Chak
Sam Chak 2022-5-13
Please note that sm has some repeated values.
Psi = -0.06-1.16i;
ym = [-0.41+0.41i, 0.54-0.58i, -0.62-0.71i, 0.64+0.56i, -0.70+0.75i, 0.68-0.60i, -0.54-0.55i, 0.43+0.79i];
sm = [0.70+0.70i, -0.70-0.70i, -0.70+0.70i, 0.70-0.70i, 0.70+0.70i, -0.70-0.70i, -0.70+0.70i, 0.70-0.70i];
fcn = (abs(Psi*ym - sm)).^2
[fmin, idx] = min(fcn)
sm(idx)
chaaru datta
chaaru datta 2022-5-13
Yes sir ...."sm" has some repeated values because its a QPSK signal and hence first four values are unique and after that same 4 values will be repeated.

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