多用戶正交分頻多工系統(MU-OFDM)是一個具有潛力的通訊技術，在未來高速無線通訊系統中扮演一個相當重要的角色。MU-OFDM系統允許多個用戶同時使用一個OFDM訊號來傳輸資料，至於如何將一個OFDM訊號的資源，包含頻寬(子載波)及功率，妥善分給多用戶使用，則是一個重要的課題。通常我們會考量的以維持用戶之間的公平原則以及提高整體的頻寬效益為主。
本篇論文主要探討的情況是，在給定傳送端的功率限制以及用戶正比公平性原則下，如何去最佳化整體用戶的總傳輸資料量。然而此議題的數學模型非常複雜難解，因此後繼的文獻著重在探討簡化複雜度的方法。其一有只針對子載波的分配，假設功率平均分配給所有的子載波，只是這樣的作法其用戶公平性的表現是比較不足的。再者是在前述的子載波配置完成後，繼續針對功率做最佳化的分佈。然而此功率分配法需利用遞迴式解根，其複雜度頗高，所以我們提出一個較低複雜度的功率分配方法，一樣也可以維持用戶之間的公平性。
我們提出的方法是針對最佳化功率分配法的非線性聯立方程式做一些變化及假設，進而推導出不需解根的次佳化功率分配公式，因而大大地降低了複雜度。
最後的模擬結果顯示我們提出的功率分配公式，在用戶之間公平性以及整體用戶的總傳輸資料量上，表現都與最佳化功率分佈相當近似，證明此方法的可行性。

Multiuser orthogonal frequency division multiplexing (MU-OFDM) is a very promising technique for achieving high downlink data rates for future wireless networks. MU-OFDM allows multiple users to transmit simultaneously on different subcarriers during the same symbol period. The resources of the MU-OFDM systems contain power and subchannels. It is important to allocate resources to multiple users fairly and to improve the bandwidth efficiency simultaneously.
The problem of maximizing the total sum of users’ data rates subject to the constraints on the total available power and the proportionality among users’ data rates is known to be NP-hard. In the previous literature, a suboptimal subcarrier allocation algorithm with equal power distribution was provided but the fairness is rough. Based on this subcarrier allocation algorithm, an optimal power distribution technique given the fixed subcarrier assignment was also presented previously to maximize the overall data rates given the power and proportional rate constraints among users. However, it required complex iterative root-finding method to achieve the goal.
In this thesis, with the above-mentioned subcarrier allocation and constraints, we propose a closed-form formula for suboptimal power distribution in MU-OFDM systems that reduce the computational burden and require no iterative operations. By computer simulations, we show that the proposed suboptimal power allocation method achieves almost the same overall capacity as the optimal method and fairness among users can also be assured.

[1] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multicarrier OFMD with adaptive subcarrier, bit, and power allocation,” IEEE J. Select. Areas Commun., vol. 17, no. 10, pp. 1747–1758, Oct. 1999.

[2] L. Chen, B. Krongold, and J. Evans, “An adaptive resource allocation algorithm for multiuser OFDM,” in Proc. IEEE Commun. Theory Workshop, Australian, Feb. 2006, pp. 143-147.

[3] W. Rhee and J. M. Cioffi, “Increasing in capacity of multiuser OFDM system using dynamic subchannel allocation,” in Proc. IEEE Int. Vehicular Tech. Conf., Tokyo, Japan, May 2000, vol. 2, pp. 1085–1089.

[4] J. Jang and K. B. Lee, “Transmit power adaptation for multiuser OFDM systems,” IEEE J. Sel. Areas Commun., vol. 21, no. 2, pp. 171–178, Feb. 2003.

[5] I. C. Wong, Z. Shen, B. Evans, and J. Andrews, “A low complexity algorithm for proportional resource allocation in OFDMA systems,” in Proc. IEEE Workshop on Signal Processing Systems, Oct. 2004, pp. 1-6.

[6] Z. Shen, J. G. Andrews, and B. L. Evans, “Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp. 2726-2737, Nov. 2005.

[7] T. S. Rappaport, Wireless Communications: Principles and Practice. Upper Saddle River, NJ: Prentice-Hall, 2002.

[8] T.M. Cover and J.A. Thomas, Elements of Information Theory. Wiley, New York, NY 1991.

[9] IEEE Standard for Local and Metropolitan Area Networks-Part 16: Air Interface for Fixed Broadband Wireless Acess Systems, IEEE Standard 802.16, June 2004.

[10] WiMax Forum, “IEEE 802.16a standard and WiMax igniting broadband wireless access,” White Paper, Sep. 2003.