Amidst conflicting views about whether soft cooperative energy detection scheme (SCEDS) outperforms hard cooperative energy detection scheme (HCEDS) greatly in cognitive radio, we establish the bridge that mathematically connects SCEDS and HCEDS by closed approximations. Through this bridge, it is demonstrate that, if the number of detectors of HCEDS is 1.6 times as that of SCEDS, they have nearly the same performance which is confirmed by numerical simulations, enabling a quantitative evaluation of the relation between them and a resolution of the conflicting views.

In this paper, we focus on the adaptive resource allocation issue for uplink OFDMA systems. The resources are allocated according to a proportional fairness criterion, which can strike an alterable balance between fairness and efficiency. Optimization theory is used to analyze the multi-constraint resource allocation problem and some heuristic characteristics about the optimal solution are obtained. To deal with the cohesiveness of the necessary conditions, we resort to bargaining theory that has been deeply investigated in game theory. Firstly, we summarize some assumptions about bargaining theory and show their similarities with the resource allocation process. Then we propose a priority-ranked bargaining model, whose primary contribution is applying the economic thought to the resource allocation process. A priority-ranked bargaining algorithm (PRBA) is subsequently proposed to permit the base station to auction the subcarriers one by one according to the users' current priority. By adjusting the predefined rate ratio flexibly, PRBA can achieve different degrees of fairness among the users' capacity. Simulation results show that PRBA can achieve similar performance of the max-min scheme and the NBS scheme in the case of appropriate predefined rate ratio.