衰減通道中直序-分碼多重存取系統下數位碼追蹤迴路之效能分析

Performance and Analysis of Digital Code Tracking Loops for DS-CDMA systems over Fading Channels

蔡宗樺(Tsung-Hua Tsai)

指導教授 ： 吳燦明

中原大學/工學院/電機工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600609

摘要

中文摘要

論文中，處理直序展頻系統訊號同步問題的非同調數位延遲鎖相迴路(digital delay lock loop)將在Nakagami-m衰減通道中，討論、分析其統計特性。基於Chapman-Kolmogorov方程式所推導出以時差為變數的機率密度函數(PDF)，包含一階迴路以及二階迴路在內，其統計特性例如時均方偵測誤差(mean square tracking error)的特性極限Cramér-Rao lower bound (CRLB) 等都會在文中提及。對於不同環境參數影響系統之追蹤誤差變異數，其數值模擬也將驗證之，追蹤誤差變異數所對應之CRLB數值分析結果亦以時域計算、模擬之。

承Nakagami-m衰減通道中相同分析流程，在頻率選擇的Rayleigh衰減通道中，直序展頻系統訊號利用非同調數位領先—落後時差檢測器加上嵌入耙式接收機方案，將討論其效能並分析之。接著介紹並推導最後封閉(Closed form)解描述的Chapman-Kolmogorov方程式推導出以時差為變數的機率密度函數(PDF)，同樣的一階迴路及二階迴路情形都將在文中探究。鎖相迴路之追蹤誤差的統計特性包含時差跳動特性及其CRLB等都詳盡探究之。最後，理論分析上的穩態時差機率密度函數之最後封閉解表示式和平均失鎖時間(mean time to lose lock)以及時均方偵測誤差與其相對應系統效能極限CRLB都將透過計算機模擬驗證之。

除此之外，數位延遲鎖相迴路裝置沉浸在都普勒飄移(Doppler shifts)環境效應中的追蹤效能分析也都一一被探究在Nakagami-m衰減通道以及頻率選擇Rayleigh衰減通道中。

關鍵字

同步 ； 時均方偵測誤差 ； 展頻

並列摘要

In this thesis, statistical analyses of a non-coherent digital delay-lock loop (DDLL) for direct-sequence spread-spectrum (DS-SS) signals over Nakagami-m fading channels are discussed. Analytical expressions to the characteristics, such as Cramer-Rao lower bound (CRLB), of the timing tracking errors have been proposed based upon the timing error probability density function (PDF) of the Chapman-Kolmogorov (C-K) equation of the first- and second-order loops. Furthermore, mean square tracking errors (MSTEs) against distinct parameters are also simulated, while their corresponding numerical results with CRLBs are confirmed by time-domain computer calculations.

Consequently, over frequency-selective Rayleigh fading channels, the performance of a non-coherent digital early-late timing error detector (EL-TED) with a RAKE scheme for direct-sequence spread-spectrum (DS/SS) signals is discussed. Closed-form expressions for the transition timing error probability density function (PDF) of the Chapman-Kolmogorov (C-K) equations of the first- and second-order loops are derived. The statistics of the tracking error are scrutinized, such as timing jitter and CRLB. Moreover, analytical expressions for the steady-state timing error PDF, the mean time to lose lock (MTLL) and the MSTE with its corresponding CRLB are verified via computer simulations.

Meanwhile, the tracking performance of the DDLL in the presence of Doppler shifts is also examined under the Nakagami-m fading and frequency-selective Rayleigh fading environments.

並列關鍵字

mean square tracking error ； synchronization ； spread spectrum

參考文獻

[1] R. C. Dixon, Spread Spectrum Techniques. New Yourk, NY: IEEE Press, 1976.

[2] P. L. Pickholtz, D. L. Schiling, and L. B. Milstein, ``Theory of spread-spectrumcommunications - a tutorial,' {em IEEE Trans. Commun.}, vol. 30, pp. 855--884, May 1982.

[6] C. R. Cahn, D. K. Leimer, C. L. Marsh, F. J. Huntowski, and G. D. Larue, ``Software implementation of a PN spread spectrum receiver to accommodate dynamics,' {em IEEE Trans. Commun.}, vol. 25, pp. 832--839, Aug. 1977.

[8] J. K. Holmes and L. Biederman, ``Delay-lock-loop mean time to lose lock,' {em IEEE Trans. Commun.}, vol. 26, pp. 1549--1557, Nov. 1978.

[9] M. K. Simon, ``Noncoherent pseudonoise code tracking performance of spread spectrum receivers,' {em IEEE Trans. Commum.}, vol. COM-25, pp. 327-345, Mar. 1977.