利用次Nyquist取樣方式於寬頻頻譜感知: 預決策與頻譜估計

Wideband Spectrum Sensing with Sub-Nyquist Sampling: Predecision and Spectrum Estimation

謝珽宇(Ting-Yu Hsieh)

指導教授 ： 劉俊麟

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202103159

摘要

隨著壓縮感知理論的興起，基於次Nyquist取樣的寬頻頻譜感知再訊號處理領域變成一個熱門的研究主題。然而，大部分已知的方法並沒有事先確認在觀測的頻寬內是否存在主要用戶的訊號而是直接將主要用戶訊號的頻譜復原。而如果整個頻寬內並沒有包含任何訊號並且接收到訊號只包含雜訊的話，直接尋求訊號頻譜可能會導致錯誤的估測結果並且浪費運算資源。為了解決這些問題，PCER探測器被提了出來。然而我們發現PCER探測器並不適用於訊號有包含高斯程序的情況。因此我們提出了一個新的預決策探測器，新的探測器能夠處理上述PCER探測器無法應付的情況。在進行預決策後，會接著進行頻譜估測。我們利用Multitaper的概念提出了一個新的頻譜估測方法，經過一些數學推導後，我們發現欲估測的頻譜可以由簡單的最小平方法得到。整體而言，整個寬頻頻譜感知系統可以分為三個部分，次Nyquist取樣，預決策，頻譜估測。

這篇論文主要分成兩個部分。第一個部分為提出的預決策探測器的介紹，我們利用次Nyquist取樣點來得到我們的檢驗統計量，再進行一些數學運算後，可以得到最後的決策結果。我們也推導出了決策閾值和偵測機率的解析解。模擬結果顯示了新的探測器能在很大的雜訊比範圍內診測到主要用戶訊號的存在，並且能夠解決高斯程序無法被偵測的問題。

第二個部分為提出的頻譜估測方法的介紹。利用Multitaper的觀念，我們推導出收到的次Nyquist取樣點和訊號頻譜之間的關係，並且我們發現頻譜能夠利用最小平方法來進行還原。為了使估測的頻譜具有唯一性，我們也介紹了基於最小尺刻度問題的一種Multicoset取樣方式。模擬結果驗證了理論推導的正確性，並且顯示出了提出的方法能在雜訊比很低的情況下有很好的性能，能夠有效的對抗雜訊。

關鍵字

寬頻頻譜感知 ； Multicoset取樣 ； 預決策 ； Multitaper ； 最小平方法 ； 尺刻度問題

並列摘要

With the rise of compressed sensing theories, wideband spectrum sensing based on sub-Nyquist sampling has become a popular topic in signal processing. However, most of the existing methods do not distinguish if primary users (PUs) are present or absent in the concerned spectrum band and directly recover the power spectrum of the PUs signals. This may lead to wrong estimation results and a waste of computational time if the concerned spectrum band is vacant and the received signal only contains noise. To address the issue, a pairwise channel energy ratio (PCER) detector, one of the predecision algorithms, was proposed by T. Xiong et al. in 2017. However, PCER detector is not suitable for the PU signals that contain Gaussian process. Hence, we proposed a new predecision detector, which uses the noise power estimated by the one-bit noise estimator to achieve better performance than PCER detector and deal with the Gaussian process issues. After predecision, power spectrum reconstruction is conducted. We use the concepts of multitaper to propose a new power spectrum estimation method. In general, the new wideband spectrum sensing system consists of three parts, which are sub-Nyquist sampling, predecision, and spectrum estimation.

This thesis is divided into two parts. The first part is the introduction of the proposed predecision detector, we construct the test statistics from the sub-Nyquist samples, and after some numerical operations, the decision result is obtained. The decision threshold and detection probability are also derived in closed forms. Simulation results are shown that the proposed detector can detect the existence of PU signals in a wide range of SNR and can deal with Gaussian process issue.

The second part is the introduction of the proposed spectrum estimation method. By using the concepts of multitaper, the relationship of obtained sub-Nyquist samples and power spectrum is derived, and we found that the power spectrum can be recovered by using the least-squares method. The multicoset sampling pattern is introduced based on the so-called minimal sparse ruler problem to the uniqueness of the recovered power spectrum. Simulation results are presented to verify the theoretical derivation, and the proposed method is shown to have good performance under low SNRs.

並列關鍵字

Wideband Spectrum Sensing ； Multicoset Sampling ； Predicision ； Multitaper ； Least-Squares Method ； Sparse Ruler Problem

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