Perfect channel estimation vs Practical channel estimation

This question is regarding nrPUSCH throughput example given below.

https://in.mathworks.com/help/5g/ug/nr-pusch-throughput.html

I tried to change different channel models with higher delay spreads (order of micro seconds) and Doppler values (greater than 2000Hz). For some of the NLOS channel models, the perfect channel estimation is giving me error. It says that timing offset should be less than or equal to minimum CP length. If I keep the offset value equal to CP length it was working. But there is a huge difference in SNR (around 10dB) for practical channel estimation and perfect channel estimation for same BLER. Also it was observed that the practical channel estimation doesn't give proper result after reaching certain BLER. The curve flattens in practical channel estimation, where as in perfect channel estimation, it is observed that the BLER values falls further.

How to overcome timing offset error in perfect channel estimation for higher delay spreads and high Doppler shifts ? Can you please clarify the algorithms used for perfect channel estimation and practical channel estimation ?

Answer 1

[Balavignesh]

Hi Pavan,

It is my understanding that when you are trying to change the channel models with higher delay spreads and doppler values, you are encountering timing offset error. In a real-world scenario, the received signal may be delayed due to various factors, such as multipath propagation. This delay is represented as a timing offset in the simulation.

In the Perfect Channel Estimation, the channel is assumed to be known without error, hence the timing offset must be less than or equal to the CP length. If the delay spread of the channel is too large (i.e., larger than the CP length), the perfect channel estimation will not work correctly, as it does not take into account the ISI caused by the large delay spread.

To overcome the timing offset error in perfect channel estimation for higher delay spreads and high Doppler shifts, I would suggest you increase the CP length, as it will allow for larger time offsets and delay spreads.

Algorithms used for Channel Estimation:

• Perfect channel estimation: This is a theoretical method where the channel is assumed to be known without error. It does not involve any actual algorithm.
• Practical channel estimation: This usually involves sending a known reference signal and comparing the received signal with the expected signal to estimate the channel. The specific algorithm can vary. Common methods include least squares (LS) estimation, minimum mean square error (MMSE) estimation, and maximum likelihood (ML) estimation. In the example you referred, it seems like they are using LS estimation

Kindly refer to the following documentation links to have more information on the following:

• Perfect Channel Estimation: https://www.mathworks.com/help/5g/ref/nrperfectchannelestimate.html
• Practical Channel Estimation: https://www.mathworks.com/help/5g/ref/nrchannelestimate.html

Hope that helps!

Balavignesh

[PAVAN KUMAR]

Hi Balavignesh..

Thanks for the clarification. I can see that CP lengths are generated from internal functions in the above mentioned example. Can you please tell me the way to change the CP lengths to come out of this problem ? Or Can I use practical synchronization for timing offset and the channel estimation with nrPerfectChannelEstimate function ?

[Balavignesh]

Hi Pavan,

If you want to simulate a scenario with a non-standard CP length (which would be non-compliant with the standard), you would need to modify the MATLAB code to manually set the CP lengths for the OFDM modulation and demodulation functions. This would involve customizing the signal processing functions and is not straightforward as it would deviate from the standard-compliant functions provided by the toolbox.

Yes, using practical synchronization methods for timing offset correct and 'nrPerfectChannelEstimate' function channel estimation allows you to handle the timing offset in a practical manner while still assuming perfect knowledge of the channel for the purpose of estimating its effect on the transmitted signal.

But, it should be good to note that this still represents an idealized scenario for channel estimation and may not fully capture the performance degradation due to practical channel estimation errors in a real system.

Answer 2

[Carlos Lopez]

Hello Pavan,

The error you are experiencing is a limitation in nrPerfectChannelEstimate whereby timing offsets must be less than the length of the cyclic prefix. Note that this limitation was removed in R2023b.

For perfect channel estimation, the OFDM response of the channel is reconstructed from the channel coefficients (path gains) and channel filter responses (path filters) by taking the FFT of channel impulse responses. For practical channel estimation in nrChannelEstimate, the algoritm is based on the reference below with some modifications.

Van de Beek, J.-J., O. Edfors, M. Sandell, S. K. Wilson, and P. O. Borjesson. “On Channel Estimation in OFDM Systems." Vehicular Technology Conference, IEEE 45th, Volume 2, IEEE, 1995.