Hello,

I wonder how 2x4 (2 Rx, 4 Tx antennas) MIMO (TM 3 and 4) may actually work:

Generally the transmission - reception chain can be modelled with the following matrix multiplications:

r = W+ E H W s

s ... transmit symbol vector

W ... precoding matrix

H ... channel matrix

E ... equalizer matrix

W+ ... pseudoinverse of W

r ... received symbol vector

The equalizer matrix E suffers from noise and interference, but, in the ideal case, equals the pseudo-inverse of H, i.e. E = H+.

In the case of 2x2, 4x2 or 4x4 MIMO the product H+ H is (ideally) very close to identity, so things work fine.

But now consider 2x4: H is a 2x4 matrix, H+ is 4x2, so H+ H is 4x4. And it is very very far from identity. The simple reason being that calculating the pseudo-inverse of a 2x4 matrix is an under-determined problem. It is impossible to make H+ H close to identity for an arbitrary H in that case.

So based on the above model, it is mathematically impossible to do proper channel equalization for 2x4 MIMO.

How is it solved technically in real life then? Or does 2x4 simply not exist and is handled as 2x2? But what do I do with the remaining two Tx antennas then, how do I shrink H from 2x4 to 2x2 and what do I do with W (being 4x2)? And how would I model the potential Tx diversity gain? Or is it the wrong model?

Any help is very much appreciated!

cheers, Stefan