• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.521-529
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• 2014

In this paper we derive some optimal convex combination bounds related to arithmetic mean. We find the greatest values ${\alpha}_1$ and ${\alpha}_2$ and the least values ${\beta}_1$ and ${\beta}_2$ such that the double inequalities $${\alpha}_1T(a,b)+(1-{\alpha}_1)H(a,b)<A(a,b)<{\beta}_1T(a,b)+(1-{\beta}_1)H(a,b)$$ and $${\alpha}_2T(a,b)+(1-{\alpha}_2)G(a,b)<A(a,b)<{\beta}_2T(a,b)+(1-{\beta}_2)G(a,b)$$ holds for all a,b > 0 with $a{\neq}b$. Here T(a,b), H(a,b), A(a,b) and G(a,b) denote the second Seiffert, harmonic, arithmetic and geometric means of two positive numbers a and b, respectively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제6권11호
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• pp.3008-3025
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• 2012

In this paper, the downlink resource allocation of OFDMA system with decode-and-forward (DF) relaying is investigated. A non-convex optimization problem maximizing system throughput with users' satisfaction constraints is formulated with joint relay selection, subcarrier assignment and power allocation. We first transform it to a standard convex problem and then solve it by dual decomposition. In particular, an Optimal resource allocation scheme With Time-sharing (OWT) is proposed with combination of relay selection, subcarrier allocation and power control. Due to its poor adaption to the fast-varying environment, an improved version with subcarrier Monopolization (OWM) is put forward, whose performance promotes about 20% compared with that of OWT in the fast-varying vehicular environment. In fact, OWM is the special case of OWT with binary time-sharing factor and OWT can be seen as the tight upper bound of the OWM. To the best of our knowledge, such algorithms and their relation have not been accurately investigated in cooperative OFDMA networks in the literature. Simulation results show that both the system throughput and the users' satisfaction of the proposed algorithms outperform the traditional ones.