Channel Estimation using the PUSCHLSChannelEstimator

[reubengs]

In the [PUSCHLSChannelEstimator](https://nvlabs.github.io/sionna/_modules/sionna/phy/nr/pusch_channel_estimation.html#PUSCHLSChannelEstimator), there is a frequency averaging step as reproduced below.

# Frequency-averaging between adjacent channel estimates
 # Compute number of elements across which frequency averaging should
 # be done. This includes the zeroed elements.
 n = 2*self._num_cdm_groups_without_data
 k = int(h_hat.shape[-1]/n) # Second dimension

 # Reshape last dimension to [k, n]
 h_hat = split_dim(h_hat, [k, n], 5)
 cond = tf.abs(h_hat)>0 # Mask for irrelevant channel estimates
 h_hat = tf.reduce_sum(h_hat, axis=-1, keepdims=True) \
                / tf.cast(2,h_hat.dtype)
 h_hat = tf.repeat(h_hat, n, axis=-1)
 h_hat = tf.where(cond, h_hat, 0) # Mask irrelevant channel estimates
 h_hat = tf.reshape(h_hat, h_ls_shape)

 # The error variance gets reduced by a factor of two
 err_var /= tf.cast(2, err_var.dtype)

It seems the intention is to average the channel estimates in groups of n REs, where n is 2*self._num_cdm_groups_without_data, and there are k such groups. However, I don't understand why the denominator of the averaging operation is always 2 instead of 2*self._num_cdm_groups_without_data, even though the tf.reduce_sum is over n=2*self._num_cdm_groups_without_data REs. Similarly, why is the error variance reduced by a factor of two, but not 2*self._num_cdm_groups_without_data? Kindly share the reasoning behind this.

[jhoydis]

Hi @reubengs,

Please have a look at this notebook, where the channel estimation with cover codes is explained. This should answer your question with respect to the noise variance reduction.

I believe that the comment in the code "# Compute number of elements across which frequency averaging should
be done. This includes the zeroed elements." creates a confusion for you.

Frequency-averaging is always done over two adjacent channel estimates. However, depending on the number of CDM groups, there might be "zeroed" channel estimates corresponding to resource elements on which nothing was transmitted to avoid interference with other CDM groups. This is also explained in the same notebook. That means that n can be equal to 2, 4, or 6, but only 2 values along this dimension are non-zero.

Hope that answers your question.

[reubengs]

Hi @jhoydis thanks for the quick reply.

Yes, I had gone through the notebook. In that it seems the assumption is that the channel remains constant on the two REs considered.

On taking a further look at the code, I get the point about the "zeroed" channel estimates when there are more CDM groups configured than those strictly required by the number of DMRS ports. So that explains why n=2*self._num_cdm_groups_without_data is chosen instead of simply n=2, I presume.

Frequency-averaging is always done over two adjacent channel estimates.

Is this just a design choice, or is there some other fundamental reason?

[jhoydis]

You could average over more channel estimates but this requires that the channel has a large coherence bandwidth.

[reubengs]

OK, got it. Thanks again for the quick replies! Have a great day!