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標題: | 經由單位元量化雷達信號的統計量來估計單一靜止目標的距離 Range Estimation for Single Stationary Target via Statistics of One-Bit Quantized Radar Signals |
作者: | Zi-Min Lin 林子閔 |
指導教授: | 劉俊麟(Chun-Lin Liu) |
關鍵字: | 單位元量化,Price 定理,範圍估計,HELEN 演算法,雷達訊號處理,統計訊號處理,分數傅立葉轉換, One-Bit Quantization,Price’s Theorem,Range Estimation,HELEN Algorithm,Radar Signal Processing,Statistical Signal Processing,Fractional Fourier Transform (FRFT), |
出版年 : | 2020 |
學位: | 碩士 |
摘要: | 在本研究中我們考慮的雷達傳送波型為線性調頻連續波形(LFMCW),我們會對帶有高斯雜訊所干擾的接收訊號進行訊號處理,並且估計出一個靜止目標物的範圍資訊,然而,在實際應用時會將接收到的訊號經過一個類比數位轉換器(ADC),這會把訊號由連續時間的訊號轉換為離散時間的數位訊號,而且轉換後的數位訊號會是原始訊號量化後的形式。 因此量化後的訊號會存在量化的誤差,這會取決於量化階層的數目,若量化階層數越高,則可以獲得越接近原始連續時間訊號的樣貌,不過這可能會導致我們需要更多記憶體空間存放資料且類比數位轉換器的硬體實作成本可能會增加,甚至會有比較高的功率消耗,所以我們便專精於研究如何透過擁有最大量化誤差的單位元類比數位轉換器(One-Bit ADC) 所轉換後的訊號進行訊號處理並估計出目標物的範圍。 為了獲得更好的估測性能,在'One-Bit Digital Radar'中推導出了單位元類比數位轉換器所轉換後的一階統計量訊號的數學式,該作者的做法是利用一階統計量訊號進行目標物的估測,除此之外,我們也可以先研究One-Bit ADC 轉換前與轉換後訊號之間的關係來幫助我們在只能取得單位元類比數位轉換器後的量化資料的情況下還原出未量化的訊號。 而對於單位元類比數位轉換器轉換前與轉換後的二階統計量之間的關係可以由反正弦定理(Arcsine Law) 以及Bussgang 定理(Bussgang Theorem) 得出,由於這兩個定理有假設原始的未量化訊號必須為零均值的高斯雜訊,但在實際的雷達波型中,其訊號可能是非零均值,所以我們的研究從Price 定理(Price's Theorem) 中推導出了一個能夠應用在雷達訊號上的定理,該定理稱為Hermite定理(Hermite Law)。 Hermite定理說明了只要原始的未量化訊號為一個雷達傳送波形加上一個平均值與變異數未知的雜訊且該雜訊為廣義平穩的高斯隨機程序,便可獲得單位元類比數位轉換器轉換前與轉換後的二階統計量之間的關係式。 接下來,我們會使用Hermite 定理還原出的未量化的二階統計量訊號來幫助我們估測目標物的範圍資訊,而這一系列的估計方式以及我們提出的演算法稱之為HELEN 演算法(HErmite Law EstimatioN Algorithm) ,在HELEN 演算法中我們使用了分數傅立葉轉換以及拍頻的方法估計出目標物的範圍資訊,而在最後的模擬結果中我們會展示調整多種不同參數下,比較使用二階統計量訊號進行估測的HELEN演算法的估計性能以及使用一階統計量訊號進行估測的估計性能之間的差異。 In this study, the radar transmission waveform we considered is LFMCW. We will process the received signal that interference by Gaussian noise, and estimate the range information of a stationary target. However, in practical applications, the received signal is passed through an analog-to-digital (ADC) converter. This will convert the signal from a continuous-time signal to a discrete-time digital signal, and the converted digital signal will be the quantized form of the original signal. Therefore, there will be a quantization error in the quantized signal, which will depend on the number of quantization levels. If the number of quantized levels is higher. The appearance closer to the original continuous-time signal can be obtained. But this may cause us to need more memory space to store data and the hardware implementation cost of the ADC converter may increase. There will even be relatively high power consumption, so we specialize in studying how to process the signal converted by the one-bit ADC converter with the largest quantization error and estimate the range of the target. In order to obtain better estimation performance. The mathematical equation of the first-order statistic signal after conversion by one-bit ADC is derived in 'One-Bit Digital Radar'. The author's approach is to use first-order statistics signals to estimate the target. Besides, we can also study the relationship between the pre-conversion and post-conversion signals of the one-bit ADC to help us restore the unquantized signal when only the quantized data after the One-Bit ADC converter is obtained. The relationship between the second-order statistics before and after the conversion of one-bit ADC can be obtained by arcsine law and the Bussgang theorem. Since these two theorems assume that the original unquantized signal must be zero-mean Gaussian noise. But in the practical radar waveform, the signal may be nonzero-mean, so our research has derived a theorem that can be applied to radar signals from Price’s theorem, which is called Hermite law. Hermite law shows that as long as the original unquantized signal is a radar transmission waveform added noise with unknown mean and variance. The noise is a wide-sense stationary Gaussian random process, the relationship between the second-order statistics signals of the pre-conversion and post-conversion signals of the one-bit ADC can be obtained. Next, we will use the unquantized second-order statistics signal restored by Hermite law to help us estimate the information of the target range. This series of estimation methods and our proposed algorithm is called HErmite Law EstimatioN (HELEN) Algorithm. In the HELEN algorithm, we use the FRFT and beat frequency methods to estimate the information of the target range. In the final simulation results, we will show the adjustment of many different parameters. Compare the difference between the estimation performance of the HELEN algorithm estimated using second-order statistics signals and the estimation performance estimated using first-order statistics signals. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/54184 |
DOI: | 10.6342/NTU202002315 |
全文授權: | 有償授權 |
顯示於系所單位: | 電信工程學研究所 |
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