If you do not have  idea of what model is appropriate , may be the best solution ( before adaptive) is to decide if your system is linear . So you can couple each input to each output by zeroing the remaining inputs so that you have an 8x 3 matrix. So tou can generate each input ( the other seven being zero) by simple sinusoids fof different frequencies reasonably separated. For instance, yo generate input u1 at frequencies w1, w2, ... wn,,and you measure the outputs of each chanel for each frequency: y1(w1), y1( w2), y1(w3) ,....., y8(w1), y8(w2) , y8(w3),  .  So you try to implement the response of each output for each input and to try to model this by a low-order filter ( for instance, according to the rules of Bode´s locus)- I mean , as lower order  as posiible but without loosing relevant information- This is only necessary on the range of frequencies you are interested( but maybe some larger range since you are then using adaptive which can probably generate high- frequency transients during the adaptation process which can excite modes which have not been modeled in the initial simple model). Thus your configuration before adaptive would be 24 frequency responses -close to transfer functions -each one of as reasonably  lower- order as possible. This can be an approximate model and procedre  to start.

This idea could also be used if the system is nonlinear and you know some operation point ( or an approximate one) of interest. So, you can proceed as above  to obtain linearized models ( transfer functions) around  such a point.

First of, MIMO is not a big deal if the unknown system is linear. All adaptive filtering algorithms are extendable to MISO form and it is straight forward to combine a few of them to make it MIMO. So two main problems remain:

1. Unknown nature of the system. Initially you can assume the unknown system to be linear and try to identify it with MISO adaptive filter. 

2. Non-stationary nature of the signal. If the input signals are available, try to figure out if the non-stationary nature is rapid or slow? This will help you get hold of the window for which you can assume the data to be stationary. 

Is the question: Can any improvement be achieved by

altering the coupling coefficients over your 8 inputs in

response to information gained at a later point in your

signal chain? If that's  the case your MIMO becomes a

"MIMIMO", inasmuch as you'll now need further inputs

to vary these coefficients using active circuitry such as

variable-gain amplifiers, or passive attenuators which

can be switched in fairly large steps (such as 3dB) to

minimize BER. What is the channel frequency at this

point in the signal chain?

In a clever scheme (yet-to-be-invented, I think) maybe

the way to go is to revert to a MIMO using AC-coupled

inputs and use the same input nodes to deliver (say)

the control voltages for the corresponding VGAs. I can

certainly help with these ICs.

Barrie

I should have said "deliver the control CURRENTS, since

of course a pure voltage source would "short the AC". In

facr, it would probably be a control voltage delivered via a

relatively large resistor (several k-ohms).

Mohammed:

You may want to try using subspace state space system identification algorithms. They are very robust and easy to use. However, you may want to try a recursive version introduced by Guillaume Mercere (University of Poitiers, France). 

Jose Ramos