Polynomial Methods to calculate Cancellation Carriers

This is a subproject to calculate Cancellation Carriers the polynomial way. A detailed article is currently only available in german. Sourcecode is provided in package 'polyofdm.cc.full' and 'polyofdm.cc.powercontrol'.

If you have n additional OFDM-Carriers for usage as Cancellation Carriers, you can enforce a decay of order 1/Δω^(n+1). But attention should be paid to the power usage of your Cancellation Carriers. If you want to enforce a high order of decay, but your cancellation carriers are not well located in frequency domain, this would require a lot of energy. Sourcecode for this method is provided in package 'polyofdm.cc.full'.

In praxis you should use a power controlled version. The problem in this case is, that you want to suppress the worst polynomials orders first. You don't want to spent a lot of energy on less interfering orders. Sourcecode for this method is provided in package 'polyofdm.cc.powercontrol'. You can choose the maximum of power you want to use. You can also limit the additional degrees of decay to a arbitrary number lower than n.

Currently this calculations could only be used with rectangular windowed OFDM (with or without zero prefix). Cyclic Prefix could not be used, since orthogonality of the carriers is not given over the full length of interval.

Following charts demonstrates the power usage of the cancellation carriers. There are 36 modulated OFDM-Carriers and 12 Cancellation Carriers. The Cancellation Carriers are not well located in frequency domain. They are only positioned in the usually used guard bands. On both sides the cancellation carriers are located in direct neighborhood without space between. The functions displayed in the chart are all basis-functions along with the cancellation of the basis-functions.













If you have a lot of carriers, you have perhaps another problem. The calculation uses the order of decay as optimization criterion. But this says perhaps less on the near field in the direct neighboring channel. Perhaps you could apply the method two times only on several carriers on each tail of the signal.