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Cognitive radios hold tremendous promise for increasing the spectral efficiency of wireless communication systems. In this paper, an adaptive bit allocation algorithm is presented for orthogonal frequency division multiplexing (OFDM) CR systems operating in a frequency selective fading environment. The algorithm maximizes the CR system throughput in the presence of narrowband interference, while guaranteeing a BER below a predefined threshold. The effect of imperfect channel estimation on the algorithm's performance is also studied.