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In cognitive radio networks, it is important to effectively use the under-utilized spectrum resources without affecting the primary users. In an underlay system, secondary users are allowed to share the channel simultaneously with primary users (with the restriction on interference level) but not in an overlay system. In this article, we consider a system where a secondary user can switch between overlay and underlay modes of operation in order to improve its throughput with limited sensing capability (i.e. sensing only one channel at a time). The results based on Markov chain analysis are satisfactorily verified using Monte-Carlo simulation. It is found that proper selection of transmission mode can provide greater improvement in throughput for a secondary user. The mode selection depends on the transition characteristics of primary users and the throughput ratio between the two modes of operation.