在使用正交分頻多工技術的感知無線電 (Cognitive Radio, CR) (Orthogonal Frequency Division Multiplexing, OFDM) 系統中，我們提出了基於子空間下的旁瓣干擾抑制技術。因為OFDM在使用頻譜上的靈活性和適應性，使其常被使用在CR系統中。當主要使用者 (Primary Users) 即所謂的合法使用者被偵測到正在使用某些子頻帶時，次要使用者 (Secondary Users) 或稱非頻帶擁有者可以簡單的關掉某些相對應子頻帶中的子載波來避免干擾。但是，由於相鄰子載波散溢出來的旁瓣亦會干擾到主要使用者，這種簡單的開-關操作通常不能保證對主要使用者的低度干擾，因此我們需要更先進的旁瓣干擾抑制技術。在本文中，我們提出了一種基於子空間下的旁瓣干擾抑制技術。在傳統的系統中所有的子載波都用於資料傳輸，不同於以往我們提出的系統會把資料放到仔細選擇過的子空間中來最小化主要使用者頻譜的旁瓣輻射並在其正交子空間上加一個抵銷旁瓣的訊號。先前文獻中提到的載波相消 (Carrier Cancellation) 和保護頻帶 (Guard Band) 都是我們提出的子空間旁瓣干擾抑制技術的特例。首先，我們證明了若以干擾最小化為目標，將資料放置在適當的子空間即可不需使用額外用來抵銷旁瓣的信號，使次要使用者可以把全部的能量用於資料傳輸。因此，基於已選擇的資料子空間，我們透過求系統總速率的最大值得出最佳輸入信號的協方差矩陣。在高斯白色雜訊通道 (AWGN Channel) 模型中我們求出最佳解，而在衰弱通道 (Fading Channel) 模型下，由於問題本身的複雜度，我們退而求其有效的次佳解。在未來的延伸方面上，值得注意的是，針對目標是傳輸率最大化，抑制信號可能仍然有好處。此外為了增加空間維數與提高設計的靈活性，我們可以將提出的技術延伸至多個OFDM符號 (Symbols) 的資料子空間與相消信號的共同佳化問題。

A subspace-based sidelobe suppression scheme is proposed for interference-avoidance in orthogonal frequency division multiplexing (OFDM) cognitive radio systems. Specifically, OFDM systems have often been employed in cognitive radio systems due to its flexibility and adaptivity in utilizing certain parts of the spectrum. That is, when primary or licensed users are sensed in certain frequency subbands, secondary or unlicensed users can simply turn off the corresponding subcarriers in these subbands to avoid interference. However, due to sidelobe radiation from neighboring subcarriers, this simple on-off operation is often insufficient to guarantee low interference to primary users and, thus, more advanced techniques must be employed. In this thesis, we propose a subspace-based sidelobe suppression scheme where, instead of utilizing all available subcarriers for data transmission, we map the data into a carefully chosen subspace in order to minimize the sidelobe radiation in the primary users' spectrum and possibly impose a active cancellation signals in its orthogonal subspace. We show that the general subspace-based sidelobe suppression scheme includes as special cases the carrier cancellation and the guard band schemes previously proposed in the literature. First of all, with the goal of minimizing the interference, we show that the active cancellation signal is not needed as long as the data is placed in a properly chosen subspace. This allows secondary users to utilize all its power for data transmission. Then, based on the chosen data-bearing subspace, we derive the optimal input covariance matrix by maximizing the system sum rate. The optimal solution is derived for the case employing only the AWGN channel model whereas suboptimal solutions are proposed for the case with fading channels to reduce the complexity of the problem.
In the further work, it is worthwhile to note that, with the goal of maximizing the system sum rate, the use of suppression signals can now be beneficial.
Furthermore, to increase the dimensions and the flexibility of the design, the proposed schemes will be then extended to the case where the data subspace and the cancellation signals are jointly optimized over multiple OFDM symbols in our future investigation.

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