A question about simulation in precoded case

I’m very confused about the meaning of this sentence in 4.4.2 of 3GPP TS 38.101-4: “The above SNR definition assumes that the REs are not precoded, and does not account for any gain which can be associated to the precoding operation.” Some of the PDCCH demodulation cases have two TX antenna ports and random type I single pannel precoding is used for the simulation. If I divide the precoding weights by sqrt(2) as indicated in 3GPP TS 38.214, there seems to be a 3dB gap compared with the results provided in the technical report. If I changed the configuration to one TX antenna port case, the simulation results seem to agree well. So I check the SNR definition but can not understand the sentence above. What could be the problem? Thanks.


I am not sure about your question; are you using our simulator to verify that, or do you have your own code and you are asking a general question?

If it is in our simulator, then a normalization might be happening automatically during the precoding operation (depending on what setup you are using), and with the additional factor you are adding, you are reducing the transmit power by a factor of 2.

The definition essentially excludes any possible spatial proccesing gain in the received power due to precoding (e.g., beamforming gain) at the transmitter.


I’m asking a general question. The reasons why I doubt the 1/sqrt(2) scaling of the precoding weights are: 1. If I change the simulation configuration to one TX antenna port case, the simulation result seems to agree with the results in 3GPP technical report, which may prove that the other parts of simulation are OK. 2. For two TX antenna port case there seems to be exactly a 3dB gap to the results in 3GPP technical report. If I remove the 1/sqrt(2) scaling factor of the precoding weights, the gap is gone. But in 3GPP TS 38.214 the precoding weights are defined with the 1/sqrt(2) scaling factor. I have no idea what might be the problem with my simulation. And I can not understand that sentence in SNR definition in 3GPP TS 38.101-4. How do you understand that sentence? What do you think might be the problem of my simulation? Thanks.

I finally find out that the fading channel is not normalized as expected. Sorry that I’ve been stucked for a long time so I’m anxious to ask for help here. But I still don’t understand that sentence though I can read every word.

It is difficult to know what definition they are using exactly. However, from the statement, it seems that they are only considering large scale effects. So, I would think of it as if they are having a single antenna transmitter with a certain average transmit power, and this is then multiplied by the path loss of the channel, and then you end up with an average received power per recieve antenna. The powers over the recevie antennas are then summed up, and this gives you the numerator of the SNR.

There is also the SNR definition by the MATLAB 5G-Toolbox: SNR Definition Used in Link Simulations - MATLAB & Simulink

But there, they seem to also drop the channel effects (so it seems to be no path loss as well).

They are many ways how you can define an “SNR”. I guess in 3GPP they are relying on old definitions and you might be able to find more information in old documents (e.g., from LTE). For example, you can also find a similar definition here from LTE (section 8.1.1):

Yes, the 3GPP channel model doesn’t account for path loss. Thank you very much for the references.

You are welcome.

I’ve another general question about precoding. The channel capacity after precoding is log2(det(I+F’H’HF)) where det is the determinant, I the identity matrix, F the precoding matrix, H the channel matrix and ’ the complex conjugate transposition. If F is square unitary matrix, then log2(det(I+F’H’HF))=log2(det(F’(I+H’H)F))=log2(det(F’)det(I+H’H)det(F)))=log2(det(I+H’H)), which is unchanged from no precoding case. Have I made any mistake? If I haven’t, what is the benefit of precoding in such case?

It is correct. If you use a unitary transform here, then you will preserve the ‘relative’ eigenstructure; it is just a ‘rotation’ (note that it holds here because you are assuming an identity matrix for the source autocorrelation matrix). In practice, you want to supress the interference between the different streams using precoding, such that at the receiving side, and in the best case, you have interference-free parallel streams.

Consider the example of massive MIMO with N transmit antennas and N single antenna users. With multi-user precoding, you want each user to receive its own data, without interference from the other users. In this case, the only way a unitary precoder would achieve that, is if H has orthogonal columns. Otherwise, each user will receive its own data superimposed by interference from other users. The orthogonality, however, does not hold in general for H, meaning that the unitary precoder would not be able to suppress the interference, unless some form of cooperation is established between the users, such that a form of joint equalization is performed at the combined receving end. The rate formula you are using above would hold when such a cooperation is possible, which is generally not true for a multi-user scenario (true for single user MIMO), but then it is not really the precoding that is achieving that, but rather the joint detection.

It is possible, however, to have one of the users (streams) to be interference-free using a unitary precoder. This can achieved by choosing the precoder to the be the Q matrix of the QR-decomposition of H’ .


Thank you very much. I’m trying to understand it. I wonder if there is some channel capacity formula or optimization criteria from which I can see clearly that the optimal precoding is to minimize the interference as emphasized in the reply.

Maybe this helps:

The general capacity formula does not tell exactly us how it can be achieved, except giving us the view of having parallel channels. This then motivates the maximization of SINR and so on.

The equations at the first page is proportional to SNR. But this SNR seems to be the SNR at the receive antenna port and not the SINR. It will take some time for me to read the chapter. Thank you very much.