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A cognitive radio must be able to observe and model the channel in which it operates. As a first step to creating a truly cognitive radio, we have developed a novel technique to model wireless channels by combining a broadband channel sounder with a wireless channel genetic algorithm (WCGA). The WCGA receives a sequence of error symbols simulated from the impulse response to train a hidden Markov model (HMM) with a genetic algorithm. The HMM is a compact representation of the channel that a radio can create online and then use as the input to a cognitive process for intelligent adaptation of the radio.