tap in Equalizer MMSE

i want ask about tap in equalizer MMSE

why equalizer use tap 2M+1

and i find program MMSE equalizer
this is the program

% Channel model, multipath channel
nTap = 3;
ht = [0.2 0.9 -0.3];

L = length(ht);
hAutoCorr = conv(ht,fliplr(ht));
hM = toeplitz([hAutoCorr([3:end]) zeros(1,2*kk+1-L)], [hAutoCorr([3:end]) zeros(1,2*kk+1-L) ]);

why ht (multipath) have 3 number?????
and about matrix toeplitz, why start with number 3-end????

please help me???

hM is the auto correlation matrix.

First hAutoCorr = conv(ht,fliplr(ht)); this the autocorrelation of ht you can use xcorr(ht) instead:
hAutoCorr(3) is the maximum that should form the diagonal of correlation matrix hM
the number 2*kk+1 is the equalizer length
if 2*kk+1=5 your correlation matrix 5 x 5 matrix


R(0) R(1) R(2) 0 0
R(-1) R(0) R(1) R(2) 0
R(-2) R(-1) R(0) R(1) R(2)
0 R(-2) R(-1) R(0) R(1)
0 0 R(-1) R(-1) R(0)


in your case R(-n) = R
R(0) is the maximum which is hAutoCorr(3), R(1) = hAutoCorr(4), R(2)=hAutoCorr(5)

hope this help