Use of Long Training Field (LTF) of 802.11 standard

In 802.11a/n the preamble part has L-LTF(Legacy-Long Training Field) and HT-LTF(High Throughput-Long Training Field). I want to clarify my understanding of these two fields:

1. Are the only difference between these 2 fields are the number of subcarriers used and the symbols used?

2. This field is mainly used for Channel estimation. What method is used to do this estimation (say on our home wifi router), is it LS/MMSE/MLS or any other in 802.11a and n? If possible can you explain how is it determined?

I'm not to familiar with the HT-LTF, but OFDM channel est. is done as follows:

rx'd long training symbol ($$LTF_{rx}$$) is the tx'd LTF ($$LTF_{tx}$$) convolved with the channel:

$$LTF_{rx}(n) = \sum_{m=-\infty}^{\infty}h(m)LTF_{tx}(n-m)$$

translate this to frequency domain:

$$LTF_{rx}(w) = H(w) LTF_{tx}(w)$$

and the channel inverse is then:

$$H(w)^{-1} = \frac{LTF_{tx}(w)}{LTF_{rx}(w)}$$

• Thank you for replying @spet. I was actually more interested in knowing how the LTF (in 802.11a) or HT-LTF (802.11n) is used to do the channel estimation. What I have found from reading online journals is Least Square & Minimum Mean Square Error are the 2 methods that are mostly used. But not getting the idea how to correlate them. – Nusrat Oct 11 '18 at 0:45
• What I wrote is exactly how the Ltf is used for channel estimation. Take your known transmitted preamble and divide it (in the frequency domain) by the received preamble. This gives you your inverse channel you should apply to each Subcarrier – spet Oct 11 '18 at 5:11
• Apologizing for not understanding this at first place. Yes, I have tested this out in Matlab and it seems I can get the CSI for all subcarriers. At the same time, I understand this is one of the methods but is this the one used in commercial wifi routers using 802.11a/n ? Because in many online journals I read that Least Square or some other algorithms are used, that confused me. – Nusrat Oct 11 '18 at 21:19
• The one explained above is the least square approach and is one of the reason OFDM is advantageous - its channel equalization scheme is simple. WiFi commercial routers use a combination of the LTF and use of pilot symbols (block or comb type pilots) to estimate the channel continuously. This paper is a good overview: pdfs.semanticscholar.org/f3fa/… – spet Oct 11 '18 at 21:32
• Thanks @spet. This makes sense. Appreciate for the good reading material – Nusrat Oct 12 '18 at 5:20