# Size of channel matrix H

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• #5836
Seerwan
Participant

Dear

as far as I know that the size of channel matrix H is ( No. of the antennas at receiver (BS) X No. of the antennas at the transmitter (UE)).

However, when I need to check the size of H after running the simulator. I could not find which variable that should I print it to check the size of H. could you please show me where can I find the real size of H in the simulator. for example, if I have the following settings, 1BS with 4 antennas and 1UE with 2 antennas working at mode 4. I think the size should be H(4×2).

Regards

Seerwan

#5883

Hi,

unfortunately there are different notions of channel matrices used in the simulator. Please note that a random realization of a channel matrix is generated every subframe (TTI) such that checking the channel matrix after a finished simulation is not very representative. However, the most commonly used notion of channel matrix in the simulator is of size: number of subcarriers x number of OFDM symbols x number of receive antennas x number of spatial transmit layers, for example in your case this could be 72x14x4x2 for 1.4 MHz of bandwidth.

Although I am not sure why the channel matrix dimension is of interest for you, I advise you to check the size of one channel matrix representation directly in the code by debugging rather than after the simulation.

greetings
Stefan

#7838
Seerwan
Participant

Dear Stefan,
Stefan regarding the post above “Size of channel matrix H”. I want to see how the size of H in the channel model (Y=HX+n) increases with increasing the number of antennas for both BS and UE and sure with the bandwidth. So based on your comments the size for (4×2) antennas can be calculated as “size: number of subcarriers x number of OFDM symbols x number of receive antennas x number of spatial transmit layers, for example in my 4×2 case this could be 72x14x4x2 for 1.4 MHz of bandwidth”.

So does the size of H is (72x14x4x2= 8064)? does that mean the size of H (8064 x 8064)?

Please Stefan could you clarify more and what is the change when change when use bandwidth 20 MHz?

Many thanks for you time

Seerwan

#7852
Seerwan
Participant

Dear Stefan,
Just to add a question… why 14 ??
I read that for normal CP it would be 7, and for extended 6, so, why 14.

Regards,
Seerwan

#7942

Hi,

you indicated the size of the channel matrix correctly. In your case it would be 72x14x4x2, which means a 4-D double in Matlab. The number of 14 symbols is 2*7 for normal CP, since two slots form a subframe and our simulator works on a subframe basis.

If you change to 10MHz, only the number of subcarriers changes, the size of H would then be 600x14x4x2.

best
Stefan

#7958
Seerwan
Participant

Dear Stefan,
I highly appreciate your valuable feedback.

Stefan I have question about the mobility speed of the mobile user, why the throughput declines at high speeds?

Regards

Seerwan

#8030
Seerwan
Participant

Dear Stefan, Hope you are fine. I highly appreciate your help and to all the staff members of “Vienna simulator” and also special thanks for Prof. Markus Rupp.

Dear Stefan I have the following questions please:

1) Just I confused a bit about something regarding the size of channel matrix H, I took another example for instance 8 antennas at the base station and 4 antennas at the UE for BW 1.4 then I have calculated the size of H ( 72 x 14 x 8 x 4= 32256). So just I wonder how the simulator manage that big size of H(32256) in estimating the channel information ? does the simulator takes the matrix H for each antenna with its UEs separately and estimate matrix H or how can manage that?

2) The former example was for 1UE what is the change in the size of H if I use 2 or 3 UEs? does the size of H still same?

3) Can I consider the simulator works as a Macro cell or which cell type the simulator supports?

Many thanks

Seerwan

#8034
Seerwan
Participant

Dear Stefan, in my question (1) above regarding the big size of H, I meant how the estimator e.g. MMSE estimator can estimate matrix like this size?.Does the estimator work on all antennas at a time or on each antenna? or how ?, please could you clarify that for me?. Many thanks.

Regards

Seerwan

#8045

Hi,

1)
in LTE-A uplink, the effective channel matrix (including the precoder) from each transmission layer to each receive antenna is estimated. In case spatial correlation is ignored, this is done for each of these channels separately. Further, channel estimation in LTE is pilod aided. The channel matrix is estimated only on pilot positions and then interpolated between those pilot positions. See
https://publik.tuwien.ac.at/files/publik_241847.pdf