CIR filter w in nrChannelEstimate (practical channel estimation)

Hi, I would like to understand the CIR denoising, and how it helps in nrChannelEstimate function.

I have read the inside of the function nrChannel Estiamtion, and read these 2 documents (Channel Estimation, and lteDLChannelEstimate), I think I pretty much understand the concept of practical estimate now. (The main difference compared to the LS+linear interpolation is that the practical estimation has the noise estimation step (by averageing along the OFDM symbol then subtracting).

But when I look into the function, I saw another technique, it's the variable w, which is defined as "time-domain windowing function for CIR denoising". I know this could help to improve the performance of the estimation, but I'm not sure how it affects the results, as these 2 documents don't mention that w.

Could anyone please explain the mathematics expression and how it can improve the performance? Or could you send me some papers/documents related to it?

Thank you so much for your time 😊

Answer 1

[Govind KM]

Hi @Thien Hieu,

CIR denoising refers to the process of reducing noise in the Channel Impulse Response (CIR) estimates obtained during channel estimation, enhancing the accuracy of the estimate. Time-domain windowing functions are used for CIR denoising due to their ability to reduce spectral leakage and suppress noise components effectively. Each window function has specific characteristics that influence its effectiveness in denoising.

Here is a brief summary of the purpose of w in the nrChannelEstimate function:

• w is defined as a raised cosine window, which helps to smoothly taper the edges of the CIR, reducing spectral leakage and noise. It is extended and shifted to align it with the main part of the CIR.
• Interpolators are created for virtual pilots, which help in estimating the channel at the edges of the frequency band. This is to combat the Gibbs Phenomenon caused by the FFT/IFFT perfomed later.
• Certain processing steps are performed on the Least Squares (LS) channel estimate using the virtual pilot interpolators to widen and improve the estimate.
• An Inverse Discrete Fourier Transform (IDFT) is performed on the channel estimate to get the CIR.
• The CIR is denoised through element wise multiplication with the window w.
• A Discrete Fourier Transform (DFT) is performed on this CIR to get the denoised channel frequency response, which is then used in further processing steps.

The following paper can be referred to for a description of the basic techniques of LS estimation and CIR denoising:

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.

Hope this is helpful!

[Thien Hieu]

Thank you so much 😊 I will read about it more