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In this paper, we investigate the aggregate throughput and proportional fairness of two independent secondary user (SU) groups in a cognitive radio (CR) network. Using a continuous time Markov chain, the expression for the aggregate throughput as a function of traffic intensity, forced termination and blocking probabilities is derived. Furthermore, throughput loss of the individual SU groups is analyzed in terms of proportional fairness. The results show that as the difference between the service rates increases the fairness deviates from its ideal value and this unfairness cannot be countered by changing the arrival/access rate of SUs. For the fixed arrival rate of SU groups there exists an optimal service rate pair which maximize the aggregate throughput.