正交分頻多工系統之低複雜度功率配置演算法

Reduced Complexity Power Allocation Methods for OFDM-based Systems

包偉丞(Wei-chen Pao)

指導教授 ： 陳永芳

國立中央大學/資訊電機學院/通訊工程學系/博士(2011年)

摘要

本論文針對以正交分頻多工為基礎之系統，提出使用者的功率配置演算法讓傳輸率最大化。一般而言，此最佳化問題可以轉換成注水問題(Waterfilling Problem)，論文中，利用Lagrange乘數法發展出此功率配置問題之最佳演算法，而可利用Bisection與Subgradient方法求得最佳注水高度(Waterfilling Level)，注水高度與配置給子載波的功率有關，然而最佳注水高度是由持續地疊代更新所求得，由於大量的反覆更新，需要花費相當的計算時間以得到最佳解，所配置的功率總和才會等於總功率限制，為了減少計算時間與負擔，本論文提出及介紹了多種低複雜度功率配置演算法。

最簡單的方法為將功率平均地配置給所有子載波，由於不需要選擇子載波，且所有子載波都有相同功率，可知此方法的複雜度會非常低，且從相關文獻得知，此方法在此問題下，相對於最佳解會有不錯的成果，然而由最佳解得知，並非所有子載波都應該配置功率，此外，通道狀況越好的子載波要配置更多功率，應該透過子載波選擇後，再配置相等或不等的功率，才能有更好的傳輸率，因此本論文利用了此概念，提出了低複雜度功率配置演算法。

第一種功率配置方法，利用了”通道狀況越好的子載波，則配置越多功率”的概念，在此利用透過對偶間隙(Duality Gap)的觀察與分析，而設計了快速功率配置方法，也同時提供功率調整參數分析，並提供了參數設定範圍，在此建議範圍內，只需少量的疊代配置功率後，所提出的快速功率配置方法，即能得到近乎最佳解。

第二種功率配置方法，利用了”透過子載波選擇後，平均配置功率”的概念，也就是說，部分子載波不配置功率，總功率平均地分配給剩餘的子載波，因此如何有效率地選擇可配置功率的子載波會直接影響傳輸率，在本論文提供了”直接搜尋(Direct Search)”、”不等式條件(Inequality Criterion)”、以及” 平均運算(Averaging Operation)”，三類不同的選擇子載波配置功率的方法。

本論文則對以正交分頻多工為基礎之多載波通訊系統，設計功率配置演算法，由於不同的通訊系統有不同問題形式與限制條件，因此要考慮其差異性，設計出適合的低複雜度功率配置演算法，以下則是各章節的介紹：

第二章針對正交分頻多工系統，透過對偶間隙(Duality Gap)的觀察與分析，而設計快速功率配置方法，也同時提供功率調整參數的分析；當考慮以正交分頻多工為基礎之感知無線電網路系統時，相互干擾訊號則必須考慮在功率配置問題中，第三章則針對此感知無線電網路，設計出能同時考慮通道增益與相互干擾的功率配置方法；第四章為單載波多重存取系統之功率配置方法。在本論文中，亦考慮了單載波多重存取系統的子載波配置，藉由實驗觀察與分析，可知使用者在擁有特定數量的子載波時，可以有最大化的傳輸速率，因此在第五章即是利用此現象，設計出低複雜度的子載波配置方法，也可再利用疊代式方法增進整體傳輸率。

關鍵字

單載波多重存取 ； 功率配置 ； 子載波配置 ； 感知無線電網路 ； 正交分頻多工 ； 正交分頻多重存取

並列摘要

This dissertation presents the solutions to the power allocation problems for orthogonal frequency division multiplexing (OFDM)-based systems, including cognitive radio (CR) networks and single carrier frequency division multiple access (SC-FDMA) systems. Generally, these optimization problems can be converted into waterfilling problems subject to power constraints. Optimal power allocation methods are developed by utilizing the Lagrange multiplier method. The bisection method and the subgradient-based method are both considered as the solutions to find the optimal waterfilling level which is related to the amount of power allocated to each subcarrier. The amount of power for each subcarrier is different and varied according to the channel gain. The waterfilling algorithm indicates that we should allocate more power to the subcarriers with larger channel gains to enable higher data transmission rates through these subcarriers, and allocates less or even no power to the ones with smaller channel gains. However, the waterfilling level is updated iteratively. It may take intensive computational time to obtain the optimum solutions due to a large number of iterations.

In order to reduce the computational time and load, several reduced complexity power allocation methods are designed for different multicarrier communication systems in the dissertation. The classical suboptimal power allocation strategy is the equal power allocation method which loads the equal amount of power to all subcarriers. It needs very low computational complexity, and has competitive performance compared to that of the optimal solution. In order to improve the performance, the constant power allocation method is presented recently which only loads the equal amount of power to some selected subcarriers. A threshold is searched by different designed algorithms to select subcarriers with power. Varied computational complexities are revealed. Obviously, the performance of the constant power allocation method depends on the threshold.

Power allocation methods presented in the dissertation are developed based the concept of the existing optimal and suboptimal algorithms. The first idea is to design a novel power allocation method to load more power to those subcarriers with high channel gains. Without resorting to the water-level related calculation in the optimal waterfilling algorithm, the proposed method is to adjust the amount of power in each subcarrier directly. By the judicious design, the proposed method achieves the near-optimal solution with a low computational complexity. This method is presented in Chapter 2 for OFDM systems. The other idea is to search thresholds for allocating equal power to some selected subcarriers. The thresholds in the proposed constant power allocation methods are obtained by three different strategies which are presented in Chapter 3-5, including the direct search, the averaging operation, and the inequality criterion. More specific information for each chapter is as follows:

Chapter 2 presents a power allocation strategy for OFDM systems with resorting to the observation and analysis to the duality gap. The analysis for the selection of the power tuning parameter in the proposed strategy is also presented in Chapter 2. The proposed strategy achieves the near-optimal solution in a fast rate. Based on OFDM systems, CR networks are introduced in Chapter 3. The mutual interference should be considered in the system model when developing the power allocation method. A novel ratio parameter to indicate the quality of a subcarrier is used to develop a low complexity and efficient power allocation scheme which can select subcarriers with relatively better channel states and causing the less amount of mutual interference. With an additional discrete Fourier transform (DFT) processing preceding the conventional orthogonal frequency division multiple access (OFDMA) processing, SC-FDMA has drawn great attention in the uplink communications. In Chapter 4, a constant power allocation method by searching a threshold is presented to improve the performance for SC-FDMA systems. Chapter 5 focuses on the subcarrier and power allocation problem of maximizing total achievable rates for multiuser DFT-precoded OFDM uplink systems. Referring to the observation through the trend indicated in the simulations, selecting a specific number of subcarriers for each user would obtain the maximum rate. Based on this property, the proposed scheme is designed to assign subcarriers to users by considering the spectral efficiency enhancement. In additions, an iterative scheme is proposed for improving the performance.

並列關鍵字

Subcarrier Allocation ； Power Allocation ； Orthogonal Frequency Division Multiplexing ； Orthogonal Frequency Division Multiple Access ； Cognitive Radio ； Single Carrier Frequency Division Multiple Acces

參考文獻

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