在此論文中，我們考慮一個主要用戶與N個次要用戶在塊狀衰減(block fading)通道上分享頻寬的頻寬分享(spectrum sharing)式認知無線電(cognitive radio)網路。我們假設次要用戶在傳送端有完整的通道資訊(channel state information)，而主要用戶在傳送端只擁有部分通道資訊。我們也假設主要用戶的傳送功率為開關式功率，並且會傳送ㄧ位元旁訊息(side information)給次要用戶的傳送端。基於以上的假設，我們研究當使用機率功率分配(probabilistic power allocation)時在干擾功率(interference power)，次要用戶之中斷機率(outage probability)及平均功率限制下最大化次要用戶之系統效能。首先我們先借由機率功率隨機變數組成的一組條件機率(conditional probability)及條件平均數(conditional mean)，將機率功率分配的問題轉變成ㄧ個固定機率分配的問題。然而這是一個非凸優化問題(non-convex optimization problem)。為了解決這個非凸優化問題，我們使用凸一階近似(convex first-order approximation)方法。此外，藉由連續凸近似(succesive convex approximation)，我們提出ㄧ個經由解凸優化問題的演算法並且有很高效能的近似解。並且證明此近似解為原本問題之靜止點(stationary point)。為了更進一步降低演算法之複雜度,我們也提出了分散式(decentralized)連續凸近似演算法。在此分散式演算法中每個次要用戶傳送端需要來自其他次要用戶傳送端的少量資訊。我們的模擬結果顯示出我們所提出的兩個演算法都能達到接近最佳效能(near-optimal performance)。

In this paper, we study a spectrum sharing based cognitive radio network (CRN) where $N$ secondary users (SUs) share the same spectrum with a primary user (PU) over block fading channels. We assume complete perfect channel state information (CSI) at the secondary transmitters while only local instantaneous CSI is assumed at the primary transmitter. The PU is assumed to adopt an ON-OFF power control policy and convey this one-bit side information to all secondary transmitters. Based on these assumptions, we investigate the optimal probabilistic power allocation that seeks to maximize the system utilities for SUs subject to the primary interference power constraint, the secondary rate outage constraints and the average power constraints. The probabilistic power allocation problem was first reformulated as a deterministic power allocation problem through defining a set of weighting variables based on the conditional probability and conditional mean of the probabilistic power random variables. The resulting optimization problem, however, is still non-convex in general. To handle the non-convex constraints, we applied a conservative convex first-order approximation technique. Furthermore, by the successive convex approximation (SCA), we proposed an algorithm that provides high-quality approximate solutions via solving a sequence of convex approximation problems. Our theoretical analysis further demonstrated that the limit point generated by our proposed SCA algorithm is indeed a stationary point of the original optimization problem.
To further reduce complexity, a decentralized version of the SCA algorithm was proposed, where only a limited amount of information exchange between the secondary transmitters is required. The convergence analysis was also provided for the decentralized counterpart.
Extensive simulations validated our analyses and demonstrated that near-optimal performance is indeed achieved by both our proposed algorithms.

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