壓縮感知技術使用調變寬頻轉換器應用於寬頻頻譜掃描之研究

Abstract

隨著頻譜需求日益增加而已規劃的頻譜卻未被充分利用，提升頻譜使用率對於下世代無線通訊是重要的課題之一。頻譜掃描能夠快速且準確地找到可利用的空閒頻帶，但是當搜尋的頻率範圍很寬廣時，會因為寬頻訊號的奈奎斯特取樣率很高以致難以實現。文獻裡，調變寬頻轉換器在訊號取樣前先乘上一週期函數使得頻譜的每一部分以窄頻訊號的形式疊加到基頻，再對基頻取樣。若可從基頻訊號判別疊加的頻譜來自哪一頻段，則完成以次奈奎斯特取樣率的取樣。壓縮感知是一種尋找欠定線性系統的稀疏解的技術，用於獲取和重構稀疏或可壓縮的訊號。壓縮感知利用訊號的稀疏性，可以從相對較少的估計值來還原訊號。若訊號頻譜具稀疏性，則可使用壓縮感知技術知道調變寬頻轉換器輸出的基頻訊號是由頻寬中那些頻段的訊號組成。然而，未被充分利用的頻譜正好在頻譜上具有稀疏性，若能透過調變寬頻轉換器將無法以奈奎斯特取樣率取樣的寬頻訊號以基頻頻寬的取樣率取樣，再以壓縮感知技術判別組成基頻的頻段有哪些，即完成寬頻頻譜掃描。壓縮感知技術的回復穩定性會受回復演算法與調變寬頻轉換器的週期函數波形選擇影響。本文提出以壓縮感知理論結合Lloyd-Max量化器與向量量化的演算法設計週期函數波形，配合調變寬頻轉換器的高速電路可以有±1、定點實數或複數震幅的設計。除此之外，因為頻譜上的一個訊號源經調變寬頻轉換器可能變成兩個相鄰窄頻訊號疊加在基頻，使回復演算法忽略含能量較小的那個頻段。本文提出以相鄰成對相加方法修改回復演算法，透過修改調變寬頻轉換器週期函數的週期為基頻頻寬倒數的兩倍，使兩相鄰窄頻訊號能量差變小，再以相鄰成對相加方法修改的回復演算法判斷訊號源出現的頻段。模擬結果證實提出之週期函數波形設計與改良回復演算法可以有效降低取樣率並保持頻帶還原錯誤率。

The rapid development of wireless communications results in a great demand for radio spectrum. Unfortunately, the resource of spectrum is limited; therefore, there is no doubt that to raise the utilization of spectrum is one of the most important subjects for next generation of cellular networks. To increase the utilization of spectrum, sensing the vacant bands in the spectrum for further use has been viewed as an effective solution in literature. However, for wideband spectrum sensing, the hardware cost may be unaffordable for practical applications as sampling at the full Nyquist rate is required for signal processing. Modulated wideband converter (MWC) is an analog front end which can support sub-Nyquist rate sampling with the aid of compressive sensing (CS) for the design of modulated waveform. In this thesis, we use MWC to sample wideband signals at a sub-Nyquist rate and find the vacant bands by the orthogonal matching pursuit (OMP). Based on the optimal design of sensing matrix for CS, we propose different modulated waveforms with amplitude of ±1 and fixed-point real/complex values to achieve high accuracy of spectrum sensing. Besides, the occurrence of side-bands may be observed as the sampling rate and the period of the modulated waveform in MWC are not well matched to wideband signals. Since the direct use of OMP to the MWC with side-bands reveals severe degradation of system performance, we also propose several modified schemes of OMP with respect to the MWC with side-bands for enhancement. Simulation results indicate that the proposed modulated waveforms can have a good tradeoff between the complexity and accuracy for spectrum sensing. The modified schemes of OMP are also verified to mitigate performance degradation due to side-bands.