We propose a novel spectrum sensing technique in cognitive radio networks that provides diversity and capacity benefits using a single antenna at the Secondary User (SU) receiver. The proposed scheme is based on a reconfigurable antenna: an antenna that is capable of altering its radiation characteristics by changing its geometric configuration. Each configuration is designated as an antenna mode or state and corresponds to a distinct channel realization. Based on an abstract model for the reconfigurable antenna, we tackle two different settings for the cognitive radio problem and present fundamental limits on the achievable diversity and throughput gains. First, we explore the "to cooperate or not to cooperate" tradeoff between the diversity and coding gains in conventional cooperative and non-cooperative spectrum sensing schemes, showing that cooperation is not always beneficial. Based on this analysis, we propose two sensing schemes based on reconfigurable antennas that we term as state switching and state selection. It is shown that each of these schemes outperform both cooperative and non-cooperative spectrum sensing under a global energy constraint. Next, we study the "sensing-throughput" trade-off, and demonstrate that using reconfigurable antennas, the optimal sensing time is reduced allowing for a longer transmission time, and consequently better throughput. Moreover, state selection can be applied to boost the capacity of SU transmission.