一種使用啾聲轉換演算法為頻率擷取並應用在GPS接收器的新型快速方法

Abstract

訊號擷取在全球定位系統 (GPS) 接收器中是一個粗略的同步過程，其目的是估測偽隨機碼(Pseudo-Random Number, PRN) 的延遲和都普勒頻率。 既有文獻中的擷取方法可分為時域法和頻域法。早期的方法是在時域中計算相關函數以達到最大近似估測。 近年來擷取的方法使用快速傅立葉轉換法 (Fast Fourier Transform, FFT) 在頻域中計算相關函數以減少所需計算複雜度。 但即使是使用頻域法若要估測到幾十赫芝解析度之都普勒頻率，其所需的計算複雜度仍相當高。 此乃因為FFT是計算訊號整個頻譜,但所要的都普勒頻率範圍相對於訊號的頻譜來說相當的小。 本論文因此提出利用啾聲轉換演算法 (Chirp Transform Algorithm, CTA) 的方法來克服此問題。主要是利用 CTA 會將所有的運算功能均放在都普勒頻率的頻段上，故可降低計算複雜度或提高頻率解析度。 本論文並將以CTA估測都普勒頻率及以FFT估測PRN碼的相位兩方法相結合,形成一新的訊號擷取方法,稱之為兩階段法。 其與傳統方法相比較,計算複雜度在同一性能下將可降低。 本論文最後以運算複雜度為量測參數,使用電腦模擬來驗証本論文所提方法之優越性。

Signal acquisition in GPS receiver is a coarse synchronization process whose goal is to estimate the Pseudo-Random Number (PRN) code delay and the Doppler frequency. The acquisition methods, in literatures, are performed in either time domain or frequency domain. Early methods compute the correlation in the time domain to achieve the performance of maximum likelihood estimation (MLE). Recently, new realization techniques have been developed for computing the correlation in frequency domain via the fast Fourier transform (FFT) such that the computation complexity is significantly reduced. The approaches via the FFT, however, still require high computation complexity if one desires to estimate the Doppler frequency with its resolution up to a few Hertz. The reason is because the FFT evaluates the whole signal spectrum, but the range of possible Doppler frequency is relatively much small compared with the signal spectrum. Therefore, this thesis employs the Chirp Transform Algorithm (CTA) to overcome this drawback because the CTA evaluates only within the range of Doppler frequency. This approach can either reduce the computation complexity or increase the frequency resolution. In this thesis, we further combine together the two techniques, one using the CTA for Doppler frequency estimation and the other using the FFT for code delay estimation, yielding a new acquisition approach, referred to as the two-stage search method which, compared with traditional methods, can reduce the computation complexity. Computer simulations are also performed to demonstrate the advantages of our proposed methods.