# The use of LS estimation with Vector OFDM

I work in Vector OFDM, but I had an issue in channel estimation in that scheme. For example, I try to use LS channel estimation but I can't get the performance back. However, in conventional OFDM, I can use that estimation straightforward.

First, let me present the difference of VOFDM compared with OFDM, the V-OFDM scheme is presented as below figure:

As you see, the only difference that in V-OFDM divides the data bock into vectors and then process them by vectors.

My question is how to use channel estimation based on pilot insertion in this case ?? any channel estimator such as for example LS. I tried different inserting the pilots in similar way of that in OFDM, but I can't get the performance back !!

Thank you

• How do you insert the pilot. Suppose there is a frequency grid of 72 sub carriers allocated, now how do you place the pilots? Apr 9 '20 at 11:05
• That's what I'm asking about .. I tried inserting then, for example, 1:4:end as vector. It means when reshaping the transmitted signal, S, I insert the column vectors 1:4:end as pilots, and then use LS as receiver, but I don't get the performance back. Apr 9 '20 at 11:30
• In conventional 3gpp LTE protocol, a pilot symbol is available at every 6th sub carrier (at least, for one antenna port transmission), the other subcarriers are used for data symbol then at the received these pilots are filtered and interpolated in freuency to get an estimate of channel for all of the frequency grid, let's say in this example all of the 72 sub carriers. Then using these estimates the data is demodulated for each of the subcarriers, you could use ML or anything. In you case once you map the vectors on a frequency grid for that symbol you could find suitable placement of pilots Apr 9 '20 at 12:00
• Let's say you have 4x1 vectors, you could make every 4th subcarrier s pilot and other three are data, then interpolate as explained above and demodulate data subcarriers based on the estimates of channel at each subcarrier. Apr 9 '20 at 12:02
• @Dspguysam Thank you for your feedback ... Yep, I totally agree with you, but the problem that doesn't work !! Apr 9 '20 at 12:07

Check this paper "Low-Complexity Equalization of Orthogonal Signal-Division Multiplexing in Double-Selective Channels" Then, Modify your code following part II in that paper. It's with details there, if you got any issue, you'd let me know. Regarding the channel estimation, you follow the same way of conventional OFDM scheme except for V-OFDM you use Vectors pilots instead of symbol pilots. I means in that mentioned paper, you will have vector of size $$M$$ used as pilots.
• Again, following that paper I mentioned above, and assuming that you built the parameters in Eq. (7) correctly. let's have $U = F^M ∧^M$. So to estimate the channel of vector $x_l$ based on received vector $y_l$, you should follow this equation $h_l = inv(diag(Ux_l))*Uy_l$ . Good luck Apr 17 '20 at 10:18