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I need to use filter Matlab function to describe the following :

H: MR x MT

x: N x MT

How to use filter to get a received signal y=H*x?

EDIT 1:

I am working on a simulation OFDM system and got x as N+Ncp x MT. Of course, I can change dimension and get MT x N+Ncp, where Ncp- length of cyclic prefix and N- subcarriers.

Will be it correctly if I take a product H * x?

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    $\begingroup$ I'm a bit confused with your model. The channel matrix contains coefficients between transmit and receive antenna but has no time dimension. But then your transmitted signal has a time dimension, $N$ samples? $\endgroup$ – Engineer Nov 19 at 18:56
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    $\begingroup$ If the received signal is y=H*x, why not just calculate H*x? You just need to adjust your matrix dimensions. Why do you want to use filter? $\endgroup$ – MBaz Nov 19 at 20:26
  • $\begingroup$ @Engineer I am working on Freq.selective channel model. N is a number of subcarriers. H has the 3 dimension, H:MR x MT x N, For each N there is a H and x(vector) $\endgroup$ – Anna Koroleva Nov 20 at 7:09
  • $\begingroup$ @MBaz For H I use rayleighchan Matlab function. I can just apply ` filter(H,x(:,t)), but I need to create H` as array and then apply using filter. $\endgroup$ – Anna Koroleva Nov 20 at 7:12
  • $\begingroup$ @MBaz I added more details to explain a question $\endgroup$ – Anna Koroleva Nov 20 at 12:32
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The OFDM-MIMO channel can be modeled as:

$ \mathbf{y} = \mathbf{H} \mathbf{x} + \mathbf{w} $

where $\mathbf{y}$ is $M_RN \times 1$, $\mathbf{H}$ is $NM_R \times (N+N_{CP})M_T$, $\mathbf{x}$ is $M_T(N+N_{CP}) \times 1$, and $\mathbf{w}$ is $M_RN \times 1$. Lets break down each one now:

  • $\mathbf{y}$: the received $N$ symbols for each $M_R$ antenna.
  • $\mathbf{H}$: the channel matrix which contains a gain between each of the $M_T$ transmit antennas and the $M_R$ receive antennas. There are $(N+N_{CP})$ symbols being transmitted (symbols + length of cyclic prefix) and $N$ being received.
  • $\mathbf{x}$: transmitted $(N+N_{CP})$ symbols on each of the $M_T$ transmit antennas
  • $\mathbf{w}$: the receiver noise on each of the $N$ subcarriers and $M_R$ receive antennas

Now, you apply the channel by just using this equation. Matrix multiplies, no need to do filter in MATLAB in my opinion.

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  • $\begingroup$ I have used chan = rayleighchan(ts,fd,tau,pdb) for H, so i can't use matrix multiplication: chan*x $\endgroup$ – Anna Koroleva Nov 21 at 17:36
  • $\begingroup$ You must call rayleighchan a bunch of times then to fill in the matrix $\mathbf{H}$? $\endgroup$ – Engineer Nov 21 at 19:01
  • $\begingroup$ If that is the case, the object that MATLAB returns from rayleighchan has a field called PathGains, and that is what you should populate $\mathbf{H}$ with. After that, you may use the approach in the answer. $\endgroup$ – Engineer Nov 21 at 19:10

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