Correction to "Optimally Joint Subcarrier Matching and Power Allocation in OFDM Multihop System"
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Letter to the Editor Correction to “Optimally Joint Subcarrier Matching and Power Allocation in OFDM Multihop System” Lijie Wang, Yong Xi, and Jibo Wei National University of Defense Technology, Changsha 410071, China Correspondence should be addressed to Lijie Wang, lilywang [email protected] Received 22 June 2010; Accepted 1 August 2010 Copyright © 2010 Lijie Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In the above paper [1], the author gives that ∂Rtot,k /∂xk is always greater than 0 as (15) in [1]. However, ∂Rtot,k /∂xk should be ∂Rtot,k (P1 , P2 ) ∂xk =
B 4 In 2
×
=
2xk P1 (Ptot − P1)+σ22 Ptot (H +xk )2 − 2P1 H 2+xk2
σ22 (H +xk )2+P1 (H +xk ) σ22 (H − xk )2+(Ptot − P1)(H− xk )
B 4 In 2
2xk P1 (Ptot − P1 ) + σ22 Ptot (H + xk )2 − 2P1 H 2 + xk2
×
, H 2 − xk2 σ22 (H + xk ) + P1 σ22 (H − xk ) + (Ptot − P1 ) (1)
where Ptot ≥ P1 ≥ 0. It is observed that the denominators of (1) and (15) in [1] are the same and positive whereas the numerators are different. From (1), it cannot be assured that ∂Rtot,k /∂xk is always greater than 0, for example, when P1 → Ptot , ∂Rtot,k /∂xk < 0. Therefore, the total channel capacity is not always monotonically increasing function of xk for the given power allocation, and (16) and (17) in [1] cannot be obtained. Meanwhile, the extended proposition in [1, Section 4] does not stand.
References [1] W. Wang, S. Yan, and S. Yang, “Optimally joint subcarrier matching and power allocation in OFDM multihop system,” EURASIP Journal on Advances in Signal Processing, vol. 2008, Article ID 241378, 8 pages, 2008.
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