In this paper, the average probability of the symbol error rate (SER) and throughput are studied in the presence of joint spectrum sensing and data transmission in a cognitive relay network, which is in the environment of an optimal power allocation strategy. In this investigation, the main component in calculating the secondary throughput is the inclusion of the spatial false alarms, in addition to the conventional false alarms. It has been shown that there exists an optimal secondary power amplification factor at which the probability of SER has a minimum value, whereas the throughput has a maximum value. We performed a Monte-Carlo simulation to validate the analytical results.