Channel decomposition

[vardhini]

Hi
I am doing my project in MIMO....can anyone explain about channel decomposition theoretically???thanks in advance...

 

[David83]

Re: Channel dec0mposition

Basically, we write the channel matrix H in the form of UΣV' (where ' means complex conjugate transpose) where Σ is a diagonal matrix with diagonal elements are the eigenvalues of H. Here U and V are unitary matrices. This is called the singular value decomposition (SVD). The received vector will be in the form:

y=Hz+n

where z=Vx, and x here is the original transmit vector. Then multiplying y from the left by U', we have:

U'y=U'HVx+U'n=∑x+U'n

which is basically decomposes the channel into parallel channels whose number is equal to the number of eigenvalues of H, that is the rank of H.

Hope this helps.

 

[vardhini]

Re: Channel dec0mposition

Hi
Yes...it was really helpful David...Thank you so much...but i need some more theoretical details...like,what is the purpose of channel decomposition,by doing so what are the advantages...these things i need...
Hope that you can help me...
Thank you

 

[David83]

Re: Channel dec0mposition

The purpose is to derive the maximum capacity possible by using MIMO systems. For example, if we have Nt transmit and Nr receive antennas, and the channel matrix is full rank, then we have min(Nt,Nr) parallel channels that are interference-free. From information theory, the total capacity of such a system is the sum of the capacities of the individual channels. That is, the total capacity of a MIMO system will be min(Nt,Nr) times the capacity of a SISO system.

 

[vardhini]

Re: Channel dec0mposition

The purpose is to derive the maximum capacity possible by using MIMO systems. For example, if we have Nt transmit and Nr receive antennas, and the channel matrix is full rank, then we have min(Nt,Nr) parallel channels that are interference-free. From information theory, the total capacity of such a system is the sum of the capacities of the individual channels. That is, the total capacity of a MIMO system will be min(Nt,Nr) times the capacity of a SISO system.

Hi
Now it is clear...Bunch of thanks...

 

[vardhini]

The purpose is to derive the maximum capacity possible by using MIMO systems. For example, if we have Nt transmit and Nr receive antennas, and the channel matrix is full rank, then we have min(Nt,Nr) parallel channels that are interference-free. From information theory, the total capacity of such a system is the sum of the capacities of the individual channels. That is, the total capacity of a MIMO system will be min(Nt,Nr) times the capacity of a SISO system.

So, is the method of SVD used only for computation purposes? Does it hold any physical meaning as well? I mean, the MIMO channel still is many-to-many channel, right? Or do we do something with the Singular values obtained by the SVD to actually convert the channel to many one-to-one channels?...it is urgent...

 

[David83]

So, is the method of SVD used only for computation purposes? Does it hold any physical meaning as well? I mean, the MIMO channel still is many-to-many channel, right? Or do we do something with the Singular values obtained by the SVD to actually convert the channel to many one-to-one channels?...it is urgent...

Actually, I think it is more a mathematical model, because in practice we would use all transmit antennas together. For that purpose, there are layered space-time (ST) codings techniques, such as vertical Bell Lab LST (VBLAST), and others.