# A question about the estimation of the frequency offset

• ### Question

• These days we are working on the frequency offset based on the short training  symbols which is composed of 16 complexes. But we find that the estimation of the frequency offset here in the Sora SDK1.6 is based on the long training symbols which is composed of 64 complexes. The below shows some of the codes in the src of Sora SDK1.6

question 1: if we use the short training symbols,then we will do delayed auto-correlation with 16 complexes,so the 64 will be replaced by 16, but we noticed the comment "this is by design, to work with the LUT below". Thus shoud we change the LUT utilized below(atan64)? And if yes ,could you give us suggestion   kindly?

question2:Here in the above codes ,we can find that the max value of iFreq is 2048,and after the step of LUT ,the max value of iFreq is 180.Then what the mean of the comment "65536=2pi" is?And if we use the short training symbols ,where shoud we take of ? And could you give us some sugestion?

Thank you!

Monday, May 13, 2013 1:36 PM

### All replies

1. ATAN64(x) = arctan(x/1024) / 64 / 2pi * 65536. We uses LUT implementation for runtime speed optimization. I guess in your algorithm, you are using similar arctan formula. I suggest you first offline test your algorithm with non-optimized atan2 function in <math.h>, then consider implement it with a different LUT from our sample.
2. You can understand "65536=2pi" from above ATAN64(x) definition. It is just one kind of unit for angle. Suggestion is similar to above answer.
• Proposed as answer by Tuesday, May 14, 2013 3:16 AM
Tuesday, May 14, 2013 3:15 AM
• Hello,Qi:

Generally speaking ,we know that freqency offset estimation is quite important for OFDM systems because of the Doppler freqency and Oscillator stability.

however,in our test,we find that if we delete the both the  freqency offset estimation and compensation ,the  receive end has almost the same ability (that is to say:the numbers of good frames do not decrease obviously),does this phenomeon means that the real freqency offset in the sora hardware is relatively little in fact ?

Sunday, May 26, 2013 9:57 AM
• That means your hardware is really good enough by default. In our measurement, the carrier frequency offset (CFO) is about 45KHz using the default configuration in SORA. That is a quite small CFO. However, if you send long frames or use high modulation order, say 16QAM or 64QAM, even the small CFO will eventually decrease the performance.

Danial.F

Sunday, May 26, 2013 4:51 PM
• Thanks Danial for the explanation!

Jin_bupt, if you want to check the frequency offset between 2 SORA box, you can use 'sdscope-11a.exe' to demodulate dumped 802.11a signals, or test by 'HwVeri.exe'.

Monday, May 27, 2013 2:23 AM
• Thank you very much.as Qi mentioned ,we test the freqency offset by using the Hwveri.exe in bin file ,and the result is about 1Khz,because we apply QPSK in data segment modulation,so the system performance is quite good and the function of small freqency is not obvious.
Monday, May 27, 2013 12:30 PM