Hello, I'm learning on Multi User Detection for CDMA at home and now I'
working on MMSE

I understand that we are using MMSE for suppressing interference, thu
increasing the SINR after the Matched filter outputs. However, I can
understand the meaning of the following equation(s), taken from the boo
"Introduction to CDMA Wireless Communication by Mosa Ali Abu-Rgheff"
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We minimize the mean square error between the signal received at th
output of the matched filter with a reference

E([b-b(y])

where b is the ideal signal (training) and b(y) is the signal after th
matched filter (we may call is b_hat, but the author refers to it as b(y))

Now, the MMSE detector applies a linear transformation 'W' to minimize th
MSE.

min E(||b-Wy||^2)

where y = RAb (R = crosscorr matrix of spreading codes, A = receive
signal matrix, b = user data matrix)

Q: Is this linear transformation similar to passing b(y) through an FI
filter just like equalization? ... Setting the taps for the trainin
sequence and keeping it same for the real data?

Now the author writes,

since ||(X)||^2 = trace{X*X_transpose} = trace{cov(X)}

therefore

min E(||b-Wy||^2) = min trace{cov(b-Wy)}

Q: What is meant by trace here? and how does X*X_transpose mean covarianc
(X)

would you suggest how I implement this in Matlab?

I suppose if I understand the meaning of these equations, implementatio
in Matlab can't be too difficult.

I hope the experts can help/guide me. I'm also expecting Vladimir to hav
an opinion about this