# comparison between frequency offset estimators

I have been working frequency offset estimation in OFDM. The objective was to compare different frequency offset estimation techniques. By using MATLAB, I have simulated three different estimation techniques, namely:

• By using Pilot tones
• Using phase difference between two repetitive symbols (proposed by Moose)
• and by using a blind method (Cyclic Prefix) The comparison between these methods is done by simulating the mean square error (MSE), and below is the output figure

However, my supervisor highly recommended to do the comparison between the CFO estimation methods using another parameter rather than the MSE(without suggesting another way). Therefore, I would like to request from the respected members to suggest me alternatives that I can do the comparison.

I hope that I'm not violating the rules of this forum by asking this general question.

• I am suggesting to apply the current simulation with different channel models, that fits specific environment. Nov 12 '16 at 17:36

Well, since you simulate you could calculate the residual frequency offset which is basically the remaining CFO after correction or the difference between the true CFO and the estimated CFO.

Another thing that is often done is to give the resulting Bit Error Rate with different estimators.

But really, please ask your supervisor what he has in mind. Everything else is guessing and probably wasted time.

• +1 for mentioning BER. But isn't the residual freq. offset equal to the difference between the actual CFO and its estimation? And the MSE just the square thereof?
– Deve
Apr 27 '14 at 15:05

Other things I would want to analyze:

• How does the MSE behave for varied frequency offsets?
• What offset ranges can each algorithm tolerate?
• How quickly does each implementation converge?
• What is the implementation complexity for each method?

I'd also second Deve's suggestion to compare them in different multipath channel scenarios.

The mean square error is helpful for evaluating the precision of the estimation method and it is important to do this analysis. But in a communcation system the most important parameter is the bit error rate (BER) for a given signal-to-noise ration (SNR). While your figure tells you what CFO estimation method has the highest precision it does not tell you what precision is required in your communications system.

To answer this question you have to do end-to-end simulations where the transmitted and received bit sequences are compared and the number of bit errors is counted. In this way you can study how the remaining frequency offset affects the system performance. Of course, the expected outcome is, that the method with the highest precision performs best, i. e. results in the lowest BER. But it might turn out that the difference in precision doesn't translate into such a great difference in BER.

Additionaly you might want to study the impact of different parameters on the MSE. This could be delay spread and frequency offset, for example. Depending on the channel that is used, robustness against channel dispersion can be of great importance.

Another interesting parameter could be the mean of the estimation error. It tells you whether the estimator is biased or not.