由於近年來寬頻通訊應用對頻譜資源的大量需求，導致有限的頻譜資源變得不敷使用與擁擠，但在固定式的頻譜管理政策下，已授權使用者（或稱主要使用者）的頻譜使用率卻很低。為了解決這個問題，感知無線電（CR，cognitive radio）這種能根據所處的環境來調整自身系統的新興技術被提出，它能在不干擾已授權使用者下，使未授權使用者（或稱次要使用者）能存取已授權使用者的頻譜，進而提高整體頻譜使用率。所以在多用戶正交分頻多工（MU-OFDM，multiuser orthogonal frequency division multiplexing）之感知無線電系統中，要進一步改善頻譜使用率的一種方式就是有效率的分配能使用的有限資源，包含能存取的主要使用者子載波與每個子載波上的功率。在本論文中，基於不干擾主要使用者通訊與節省次要使用者能量的考量下，我們將針對MU-OFDM CR系統來提出數個低複雜度的資源分配演算法來分配子載波與功率。
首先，在以限制次要使用者的最高功率來保護主要使用者通訊的情況下，我們提出一個低複雜度的子載波與功率聯合分配法。若功率分配已知，我們推導出一個使所有子載波通訊容量總和最大的子載波分配規則。根據這個規則，我們著手發展出一種子載波與功率聯合分配的架構，使得通訊容量總和最佳化的過程能在子載波與功率個別最佳化之間輪流執行。若子載波分配已知，在最高功率限制下，通常會使用一套具有高複雜度的最佳功率分配演算法（即迭代式分區注水演算法）去反覆執行注水演算，來決定每個子載波上的功率是不是比最高功率還大。這樣反而讓功率分配變得沒有效率。為了讓功率分配更有效率，我們技巧地利用一些要達成最佳功率分配時所必須滿足的條件，來設計一個低複雜度的演算法以滿足每個子載波上的最高功率限制，並更新功率分配後對應的水平面。因此，我們把所提出的高效率功率分配演算法整合於子載波與功率聯合分配的架構內，以便獲得最大的通訊容量並同時降低複雜度。
為了進一步提高通訊容量，使用合作式通訊技術所帶來的空間多樣性以改善通訊品質是近年來的趨勢。但加入合作式通訊技術後，也使得推導最佳的資源分配變得複雜。為了解決此問題，我們將一個三節點中繼網路（three-node relay network）簡化成一個具有等效通道增益的兩節點網路（two-node network），並進一步利用此雙節點網路將合作式MU-OFDM CR系統的資源分配問題改寫成與未使用合作式通訊的MU-OFDM CR系統的資源分配問題類似的形式；所以我們之前基於MU-OFDM CR系統發展的子載波與功率聯合分配法可以用於決定合作式MU-OFDM CR系統的資源分配。此外，藉由等效通道增益，我們亦探討中繼點的位置對系統容量的影響：當中繼點在資訊源（source）與目的端之間的中點時，系統容量可以達到最大值；但當中繼點在資訊源與目的端的中垂線上時，系統容量對資訊源-中繼點-目的端這條線的角度很敏感，相較之下，當中繼點離資訊源或目的端很近時，系統容量對這個角度並不敏感。
最後，基於子載波的可靠度，我們也發展一個高效率的功率分配演算法。子載波的可靠度是受不完美的頻譜偵測（imperfect spectrum sensing）與主要使用者重新回來使用子載波（reoccupation）的影響。在這些情況下，次要使用者並不知道主要使用者正在使用子載波，所以次要使用者的通訊會受主要使用者的干擾而造成通訊容量損失。為了把子載波的可靠度納入功率分配的最佳化問題，我們使用上述因素的機率來找通訊容量期望值總和的最大值，而不是像傳統的功率分配最佳化問題去找通訊容量總和的最大值。基於我們所提的最佳化問題，我們亦推導出其最佳功率分配，但它必須先依據最高功率限制將分配到的子載波分成兩類，再用高複雜度的數值分析方法來解非線性的方程式以算出子載波上的功率。為了有效率地分配功率，我們首先在可靠的精確度之下，去對最佳功率分配作近似，由近似的結果，再提出一個低複雜度的功率分配演算法來更新功率分配後對應的水平面，以判定是否滿足最高功率限制。不論影響子載波可靠度的參數如何變動，使用我們所提的節能低複雜度功率分配演算法的通訊容量期望值總和能逼近使用最佳解所得的。

Cognitive radio (CR) is an emerging technology for maximizing spectrum utilization under the fixed spectrum management policy and can be adapted to a dynamic wireless environment to provide flexible wireless access. In a multiuser orthogonal frequency division multiplexing (MU-OFDM) CR system, one way to improve spectrum utilization is to efficiently allocate the limited resources, which are the available subcarriers of licensed users (also referred to as primary users [PUs]) and the allocated power on these subcarriers. Given the concerns of protecting PUs and conserving the energy of unlicensed users (also referred to as secondary users [SUs]), this dissertation addresses the resource allocation problem for MU-OFDM CR systems.
In this dissertation, we first present a joint subcarrier and power allocation (JSPA) algorithm for MU-OFDM CR systems, where a peak power constraint is used to protect PUs. For subcarrier allocation, a rule is derived to maximize the sum capacity for a given power distribution. With this rule, we form a JSPA algorithm in which the sum capacity optimization can be alternated between the subcarrier and power. To simplify the high-complexity optimal power allocation algorithm (i.e., the iterative partitioned water-filling [IPWF] algorithm) for the joint scheme, we further develop a simple method for updating the water level when each subcarrier is allocated to an SU. The proposed method to update the water level achieves a system capacity close to that of the JSPA algorithm with optimal power distribution, and with much lower computational complexity.
To study a JSPA algorithm for cooperative MU-OFDM CR systems, we simplify a three-node relay network to a two-node network with the equivalent channel gain and then formulate the resource allocation problem for a cooperative MU-OFDM CR system in a form similar to that of a non-cooperative MU-OFDM CR system. Therefore, the JSPA algorithm for MU-OFDM CR systems can be extended to the cases for cooperative MU-OFDM CR systems. The proposed algorithm achieves a system capacity close to that of the JSPA algorithm with optimal power distribution for cooperative transmission, and with much lower computational complexity. In addition, if the relay node is at the midpoint between the source and destination, the system capacity can reach its maximum value. However, when the relay is at a midway location (on the perpendicular bisector of the line segment) different from the midpoint, the capacity is sensitive to the angle of the line source-relay-destination. In contrast, when the relay is in proximity to either the source node or the destination node, the system capacity is not sensitive to the angle.
Finally, we investigate an efficient power allocation algorithm based on the reliability of subcarriers for OFDM-based CR systems. The reliability of subcarriers is affected by imperfect spectrum sensing and by PU reoccupation, which introduce interference from the PU and cause rate loss to the SUs’ transmissions. To incorporate the reliability of subcarriers into a power allocation problem, we maximize the sum expected capacity using probabilities that reflect the effects of the reliability of subcarriers, instead of maximizing the sum capacity in traditional OFDM systems. A peak power constraint is also included to protect the PUs’ communication links. Based on the modeled optimization problem, we derive the optimal power distribution, which classifies the assigned subcarriers according to the peak power constraint and then allocates power using high-complexity numerical methods to solve a nonlinear equation. To reduce the computational complexity, we approximate the optimal power allocation with reliable accuracy and then propose a low-complexity power allocation algorithm for updating the water level, which is similar to the IPWF algorithm, to determine if the peak power constraint is satisfied. The proposed energy-efficient algorithm achieves a sum expected capacity close to that of the optimal solution, but with much lower computational complexity, regardless of the change in the parameters of the reliability of subcarriers.

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