A cognitive radio opportunistically accesses spectrum bands under the constrain that it does not interfere with the licensed users. Cognitive radio performs spectrum sensing to find spectrum opportunities. Although a large number of spectrum sensing algorithms are available in literature; majority of them addressed static cognitive radios. In this paper, we study the energy detection based local spectrum sensing in the presence of user mobility. We show that CR mobility improves spectrum sensing performance by exploiting spatial diversity. We propose a framework for local spectrum sensing in which a cognitive radio do multiple spectrum measurements and makes a decision about the existence of the licensed user. An optimal fusion rule based on likelihood ratios is derived and based on test statistics a suitable detector and functional architecture of a cognitive radio is proposed. A closed form expression for the number of spectrum measurement cycles is also derived in this paper under given performance constraints. \textcopyright2010 IEEE.