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## Live Q&A - 802.11/Wi-Fi Channel Estimation

Christopher Hansen - **Recording Soon Available** - DSP Online Conference 2024

**mh**

**Christopher**Speaker

I uploaded the yCTS.mat file to github. I'm not aware of a good open source set of functions for the 802.11 PHY layer. For the legacy standards, i.e. 802.11a/g, the PHY is simple enough that you can generate the preamble using the training sequences in the standard and common features such as FFT and convolutional encoding.

**Harry**

When is Total Least Squares the right tool to use? Can you recommend any references (or share source code)?

I can see how to do an ordinary least-squares channel estimation for **y** = **Xh**, where **X** is a Toeplitz matrix of the (noise-free) TX signal. But to solve the inverse problem (to directly design an equalizer **g**), we want **Yg** ≈ **x**, where we only have *noisy* observations of **y**. Should I then use Total Least Squares?

**Christopher**Speaker

In general, Total Least Squares is preferred when there are noisy observations in both the data matrix and the observation vector. A good quick overview of this is in the paper "The Data Least Squares Problem and Channel Equalization" by R. D. DeGroat and E. M. Dowling, IEEE Trans. on Signal Processing, Vol. 41, No. 1, January 1993. p.407 - 411. For more details, I would suggest 2 books. First, Matrix Computations by Golub and Van Loan, 4th Edition. Second, The Total Least Squares Problem by S. V. Huffel and J. Vanderwalle.

**Harry**

Thank you for this really fantastic recommendation. Something feels familiar about the Data Least Squares solution - the projection onto the complement noise subspace reminds me very much of the MUSIC algorithm (and other subspace-based direction-finding algorithms used in array signal processing).

Thank you for your most enlightening presentation. Some years ago, I implemented an 802.11a/g/n/ac receiver (including MIMO) in an FPGA, but I'm not up to speed on 802.11ax/be. Do you know any books covering the new stuff, or should I just dive back into the standard?

**Christopher**Speaker

For 802.11ax/be, I think the standard is the most helpful. I'm not aware of any new books that cover the newer PHY layer.

**Christopher**Speaker

The best description is in the paper "A Least-Squares Approach to Blind Channel Identification" by G. Xu, H. Liu, L. Tong, and T. Kailath, IEEE Trans. on Signal Processing, Vol 42, No 12, December 1995.

**Mayur.S**

Christopher,

For SISO channel estimate, i think the 200 nsec delay is due to Cyclic Diversity Delay mode in 802.11n mode.

As I understand, it is using multiple antennas to transmit copies of time delayed data packets and the receiver can use multiple antennas to receive the signals. Isn't CDD also a type of MIMO mode but sending only 1 spatial stream?

I hope I was able to explain my doubt clearly.

Mayur

**Christopher**Speaker

Yes. The Cyclic Delay Diversity (CDD) is the standard mode for sending legacy packets when a device has more than one transmit antenna. It was designed both to provide diversity and to work with legacy single antenna devices.

**Mayur.S**

Christopher,

I am not able to understand how oversampling of data symbols aid blind and semi blind estimation.

Kind Regards,

Mayur

**Mayur.S**

Dear Christopher, Thank you for the talk on channel estimation.

I have seen in Wi-Fi QAM constellation diagrams, 2 pilot symbols.

Can you please explain the relevance of the pilot symbols in light of channel estimation.

Kind Regards,

Mayur

**Mayur.S**

You have answered this towards the end of your presentation :)

Thank you.

Mayur

**Christopher**Speaker

There are a number of practical issues that arise when making OFDM symbols longer and the FFT sizes larger. First, longer OFDM symbols (in time) lead to narrower sub-carrier spacing. Residual timing errors and phase noise will cause interference between sub-carriers if they are too close. Second, longer OFDM symbols require more computations to demodulate and decode. Wi-Fi packets must be fully demodulated and decoded in less than 16 microseconds so the receiver can send an acknowledgement back to the transmitter. 802.11ax already needed to add the packet extension to help with this.

**Christopher**Speaker

The pilots are normally used for tracking residual carrier frequency offset (CFO) when demodulating the data symbols. Typically, the receiver will try to estimate the CFO from the L-LTF (legacy long training field) and possibly refine that estimate on other symbols in the preamble. However, there will often be residual errors as well as phase noise that be present in each data symbol. So, the pilots can be used as phase references on each symbol to help remove these errors.

**Mayur.S**

Christopher,

The long OFDM symbol duration of 12.8 usec in 802.11ax standard improved spectral efficiency by around 20%.

Why did not the 802.11be WG further increase the OFDM symbol length by X2 or X4 to further improve spectral efficiency? Are there any limitations on FFT size on the DSP?

Kind Regards,

Mayur

**Christopher**Speaker

I have a Matlab LiveScript that I used to generate the plots and equations for the main sections of the talk here: https://github.com/covariantcorp/matlabExamples . You will need Matlab and the WLAN toolbox to run the script. For the semi-blind estimation, that will take a little more work but I will eventually put it into the same repository.

**Leonard**

Christopher, do you have the code for your session posted in a repo somewhere that you can share?

**Christopher**Speaker

The y axis is magnitude. The samples, x, are complex (I/Q) so I use abs(x) in Matlab.

**Gary**

Slide 13: Is the format of the left image of the CTS capture an AM demod (mag / mag^2)?

Hi Chris,

In your shared repos, it seems that the mat file yCTS.mat is missing. Could you please update?

Besides, the WLAN toolbox is hard to get for individuals. Do you know any open source library to replace the functions like wlanWaveformGenerator.m, wlanNonHTOFDMInfo.m etc. used in your examples? Thanks.