Among various spectrum sensing methods in cognitive
radio, the energy detection method is most popular. This
method does not require a priori information of the primary
signals and has a very easy circuit. In this paper, performance
of a cognitive radio system is analysed with the help of SNR vs
Pd curve as well as ROC (Receiver Operating Characteristics)
curve which is the graph between probability of detection and
probability of false alarm. As the probability of detection should
be high and probability of false alarm should be low, ROC gives a
trade off between the two values. To mitigate the fading effect in
wireless environment, diversity techniques are used.With the help
of diversity combining, multiple received signals are combined
into a single one. In this paper, we present and compare the
graphs of SNR vs probability of detection and ROC for energy
detector in Rayleigh fading channel with and without considering
diversity.