This page accompanies the paper
"On the general form of FIR MIMO biorthogonal partners"
by Bojan Vrcelj and P.P. Vaidyanathan

(invited paper) Proc. 35th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, Nov. 2001.



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

F00(z) = 0.2596 + 0.4772z-1 + 0.4132z-2
F01(z) = - 0.3841 + 0.4084z-1 + 0.3126z-2
F02(z) = - 0.2525 - 0.2650z-1 - 0.1502z-2
F10(z) = - 0.4951 - 0.3418z-1 - 0.3590z-2
F11(z) = 0.1961 - 0.0961z-1
F12(z) = 0.0789 + 0.2840z-1
F20(z) = - 0.0193 - 0.3184z-1 - 0.1914z-2
F21(z) = 0.2626 - 0.4502z-1 - 0.0343z-2
F22(z) = - 0.3693 + 0.1101z-1 - 0.2499z-2

As explained in the paper, the SSE version of this channel, F2(z) is obtained from F(z) after decimation by 2.

According to the algorithm implicit from the simple Bezout identity, the unitary matrix W(z) [see equation (4)] was found to be:

W(z) =     [0]                             [0]                                 [0]                             [ 1]                             [ 0]                             [ 0]
                   [0]                             [0]                                 [0]                             [ 0.7162]                   [ 1]                             [ 0]
                   [0]                             [0]                                 [0]                             [ 1.3152]                   [ 0.9048]                   [ 1]
                   [1]                             [0]                                 [0]                [-11.2639 -7.7232]  [-5.8086 -4.6116]   [-9.8319 -5.3275]
                   [0]                             [1]                                 [0]                 [33.7268 24.1971]    [20.8873 15.3348]    [26.5733 18.6778]
                   [0]                             [0]                                 [1]                 [35.4297 29.5595]    [23.6246 19.7248]    [27.6814 22.5290]
 
 
 

Similarly, the unimodular matrices U-1(z) and V-1(z) that appear in the Smith form decomposition  [see equation (7)] were chosen to be:

U-1(z) =            [1]                                                     [0]                                                    [0]                                                                 [0]                                         [0]                   [0]
                [0.9831    0.4680]                                        [1]                                                    [0]                                                                 [0]                                         [0]                   [0]
            [-0.0339   -0.0178]                         [-0.0462   -0.0009]                       [0.0288   -0.0034]                              [-0.0271    0.0114    0.0133]                 [0]                   [0]
[599.6885  850.6363  277.3421]  [864.4142  740.9418   14.3703]  [-616.8136 -374.9861   53.6704]  [545.5727  174.5229 -463.2075 -207.7911]   [0]                   [0]
               [0.7095    0.1702]                             [0.4645    0.0088]                        [-0.1939    0.0329]                             [0.8043   -0.4247   -0.1275]                 [1]                  [0]
            [-0.3582   -0.0085]                          [-0.0399   -0.0004]                      [-0.0528   -0.0016]                             [0.8185    0.2630    0.0064]                   [0]                  [1]
 

V-1(z)=        [-0.7567]             [0.4557]                        [-0.2251   -0.6335]
                                [1]         [0.5456    0.4540]        [-1.2240   -1.5503   -0.6312]
                                [0]         [-0.3615    0.9454]      [1.6305   -1.1460   -1.3143]


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Maintained by Bojan Vrcelj
Last updated October, 2001