This page accompanies the paper
"THEORY OF MIMO BIORTHOGONAL PARTNERS AND THEIR APPLICATION IN CHANNEL EQUALIZATION"
by Bojan Vrcelj and P.P. Vaidyanathan

submitted to ICC2001


The equivalent MIMO (3-by-3) channel F(z) was taken to be:

F00(z) = - 0.2101 + 0.0067z-1 + 0.2199z-2 - 0.1177z-3 - 0.4573z-4
F01(z) = 0.0357 - 0.3351z-1 + 0.2309z-2 - 0.1434z-3
F02(z) = - 0.2653 - 3.2019z-1 - 0.4438z-2 - 0.1378z-3 + 0.0520z-4
F10(z) = 0.1863 - 3.2573z-1 - 0.3591z-2
F11(z) = 0.4892 + 0.1416z-1 - 0.1555z-2 - 0.0992z-3 - 0.1915z-4 - 0.0514z-5
F12(z) = - 0.2849 - 0.4620z-1 - 0.0211z-2 + 0.1480z-3
F20(z) = 0.4235 - 0.2924z-1 + 0.1358z-2
F21(z) = - 0.1649 - 2.6988z-1 + 0.6550z-2 - 0.2351z-3
F22(z) = - 0.0458 + 0.3100z-1 - 0.7134z-2 + 0.0277z-3 - 0.4219z-4

As explained in the paper, the SSE version of this channel, F2(z) is obtained from F(z) by decimation.


According to the algorithm implicit from the simple Bezout identity, one possible FIR FSE is given by:

H00(z) = 0.0449 - 0.0008z-2 + 0.0060z-4 - 0.0036z-6 - 0.0005z-8 - 0.0003z-10 - 0.0001z-12
H01(z) = - 0.3152 - 0.0011z-2 + 0.0002z-4 + 0.0001z-6 - 0.0002z-8
H02(z) = - 0.0175 - 0.0756z-1 - 0.0089z-2 + 0.0219z-3 + 0.0113z-4 + 0.0021z-5 - 0.0004z-6 + 0.0017z-7 + 0.0007z-8 + 0.0005z-9 + 0.0001z-10
H10(z) = - 0.0361 + 0.0242z-2 + 0.0220z-4 + 0.0115z-6 + 0.0038z-8 - 0.0001z-10
H11(z) = 0.0193 - 0.0096z-2 - 0.0058z-4 - 0.0014z-6 - 0.0004z-8 - 0.0001z-10
H12(z) = - 0.3590 - 0.0987z-1 + 0.0079z-2 - 0.0474-3 - 0.0145z-4 - 0.0328z-5 - 0.0090z-6 - 0.0003z-7 - 0.0002z-8 - 0.0001z-10
H20(z) = - 0.3274 - 0.0840z-2 - 0.0638z-4 + 0.0011z-6
H21(z) = 0.0635 + 0.0212z-2 + 0.0034z-4 + 0.0021z-6
H22(z) = 0.0132 + 0.5031z-1 + 0.1467z-2 + 0.0132z-3 + 0.0010z-4 + 0.0003z-5 + 0.0028z-6 - 0.0005z-8

And finally, the third order predictor A(z) as introduced in the Section 3 of the paper and in Fig. 3(c) is given by:

A00(z) = 1.0717 - 0.0597z-1 - 0.0080z-2 - 0.0010z-3;
A01(z) = - 0.0198 - 0.0029z-1 - 0.0001z-2;
A02(z) = 0.0198 - 0.0037z-1 - 0.0011z-2;
A10(z) = 0.8191 - 0.1412z-1 + 0.0351z-2 - 0.0001z-3;
A11(z) = 0.0047 + 0.0005z-1 + 0.0001z-2 - 0.0001z-3;
A12(z) = 0.0633 - 0.0033z-1 + 0.0012z-2 - 0.0001z-3;
A20(z) = 0.2774 - 0.0999z-1 - 0.0013z-2;
A21(z) = - 0.0217 + 0.0016z-1 + 0.0002z-2;
A22(z) = - 0.0275 - 0.0007z-1 - 0.0001z-2 + 0.0001z-3;

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Maintained by Bojan Vrcelj
Last updated Feb, 2001