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The channel capacity of multi-channel cognitive radio systems is studied with the assumption of limited sensing capability. The randomness of sub-channel selection is utilized to convey information. Two types of sub-channels, memoryless and finite state, are considered. For both cases, the separation of sub-channel input distribution optimization and sub-channel selection policy optimization is proved. For the memoryless case, explicit expressions for optimal sensing policy are obtained. For the finite state case, the optimization of channel capacity is considered as a Markov decision problem that maximizes average award. By using Markov decision theory, it is shown that, for the finite state case, the channel capacity is determined by the static distribution of state.

Capacity of multi-channel cognitive radio systems: bits through channel selections