在此篇論文中，我們探討在塊狀衰減通道下N個主用戶(primary user)和N個次用戶(secondary user)及在N個次中繼站(secondary relay)的幫助下的頻譜共享式感知無線電中繼協助網路。我們考慮每個中繼站只服務特定的使用者或可以服務所有的使用者兩種應用情境。在兩種應用情境中，我們假設中繼站都以全雙工(full-duplex)及解碼前送(decode-and-forward)的協定方式運作。我們假設主要系統的傳送端只有本地通道資訊而次要系統的傳送端有完整的通道資訊(channel state information)。由這些假設，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)及功率限制下最大化次要用戶之系統效能。為了解決這個問題的非凸優性(non-convex)，我們使用凸一階近似(convex first-order approximation)方法。此外，藉由連續凸近似(successive 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。另外，為了證明此近似解為原本問題之靜止點(stationary point)，我們提出了一個次最佳的問題並驗證了此收斂證明。我們的模擬結果顯示出我們所提出的演算法在兩個應用情境中都能達到卓越的效能(superior performance)。我們也做了更多的模擬結果來探討雙工模式以及兩個應用情境的權衡關係。

In this thesis, we study a spectrum sharing based cognitive relay-assisted network (CRAN) where $N$ secondary users (SUs) share the same spectrum with a primary user (PU) over block fading channels with the aid of \( N \) secondary relays (SRs). We considered two scenarios where each relay can only serve a particular SU or can be shared by all SUs.
both scenarios are operated in full-duplex (FD) mode and decode-and forward (DF) protocol is employed.
We assume complete perfect channel state information (CSI) at the secondary transmitters (or secondary sources) and relay transmitters while only local instantaneous CSI is assumed at the primary transmitter. 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, and the secondary rate outage constraints and the individual power constraints.
To handle the non-convex constraints in the resulting optimization problem, we applied conservative convex first-order approximation techniques. 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.
To demonstrate that the limit point generated by our proposed SCA algorithm is indeed a stationary point of the optimization problem before applying convex approximation, we proposed a suboptimal scheme and verified the convergence proof.
Extensive simulations validated our analyses and demonstrated that superior performance is indeed achieved by both our proposed algorithms, where the achieved utilities are close to the optimum.
Further simulations results revealed the trade-off between duplex modes and two scenarios.

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