This paper develops a power allocation strategy for multiple networks of Poisson-distributed single antenna nodes that share the available spectrum in a spectrum underlay scenario. This strategy aims to maximize the overall throughput obtained by sharing the spectrum while limiting the degradation of the successful transmission probability of each network. In its original form, this joint power allocation problem is difficult to solve. However, we demonstrate that the problem can be transformed into a convex optimization formulation, which can be efficiently solved. Furthermore, we obtain a quasi-closed form solution that has a water-filling interpretation by analyzing the optimality conditions. Numerical results indicate that when a spectrum sharing scheme employs the proposed optimal strategy of power allocation, throughput improves substantially over that obtained by allocating the spectrum exclusively to the primary network. Moreover, when the number of spectrum sharing networks increases, the enhancement is significant, being up to the limit imposed by the maximum allowable degradation in the performance of each network.
In view of the problem that ZnO varistors are often subjected to thermal breakdown and deterioration due to lightning strikes in low-voltage power distribution systems, this article used a 8/20 µs multi-pulse surge current with a pulse time interval of 50 ms to perform shock experiments on ZnO varistors. SEM scanning electron microscope and an XRD diffractometer were used to analyze the structure of the grain boundary layer and the change of the crystalline phase material of ZnO varistor under the action of a multi-pulse current. The damage mechanism of ZnO varistor under the multi-pulse current was studied at the micro level. The results show that the average impact life of different types of ZnO varistor is significantly different. It was found that the types of trace elements and grain size in the grain boundary layer will affect the ability of ZnO varistor to withstand multi-pulse current. As the number of impulses increases, the grain structure of the ZnO varistor continues to degenerate. The unevenness of internal ion migration and the nonuniformity of the micro-grain boundary layer cause the local energy density to be too large and cause the local temperature rise to be too high, which eventually causes the internal grain boundary to melt through, and the local high temperature may cause the Bi element in the ZnO varistor to change in different crystal phases.
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