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Power allocation is an important issue for spectrum sharing of unlicensed bands, in which multiple unlicensed systems may coexist and operate. Recently some works have been reported on spectrum sharing in frequency-flat unlicensed bands. However, there has not been much work on power allocation for spectrum sharing in frequency-selective unlicensed bands. In this letter, we propose an optimal power allocation strategy on frequency-selective interference channels (IC). This strategy, also referred as general power allocation (GPA), allows the transmission power density to vary within one subcarrier. By showing the duality of frequency-selective and parallel frequency- flat channels, we can therefore compute the achievable rate region of GPA. Our method can be regarded as an extension of previous results for frequency-flat scenarios. It will also be shown that over frequency-selective Gaussian IC, the proposed GPA can achieve larger rate region than conventional power allocation strategies, where the transmission power density on each subcarrier is set equal.