在複徑衰褪的環境下非同調鎖碼迴路的功能表現

Abstract

在直接序列展頻通訊(DS/SS)系統中，吾人常以非同調鎖碼迴路( Noncoherent Delay-Locked Loop, DLL) 來追蹤偽亂碼(pseudo noise code, PN code)的相位。 然而，在無線傳輸的環境下，非同調鎖碼迴路的運作不僅受到相加性高思 白雜訊 (additive Gaussian white noise, AWGN) 的干擾， 同時也受到複徑衰退(mutipath fading)的影響。本論文主要探討的則即 是非同調鎖碼迴路在一個經簡化 後的時變通道下之行為表現。 追蹤誤差(tracking error)的暫態機率密度函數(transition probability density function) 可以數值方法 (numerical method) 求得，並可從中觀察同調鎖碼迴路是如何暫態運作。在此論文中 亦 詳述了在求解過程中所遇到的問題並提出解 決的方法。在此，我們的討論集中在兩個重要 的表現評估參數上: 一為鎖碼迴路能夠維持鎖定的時間(Mean Time to Lose Lock, MTLL)； 另一個則是追蹤誤差( tracking error)。因為相位誤差(phase error)可視為再生過程 (renewal process)，所以，再生過程法(Renewal Process Approach, RPA) 可用來分析鎖碼迴路。然而 ，在時變通道下用再生過程法並無法得到合理的參數。文末， 我們並分析了一種擁有較大的拉回範圍(pull-in range)及鎖定範圍( lock-in range)的 改良式鎖碼迴路(Improved DLL)。 Noncoherent {\it delay-locked loops} (DLL) are often employed to track the code phase of the pseudo noise (PN) sequence used in a direct-sequence spread spectrum (DS/SS) system. In a wireless radio communication environment, the performence of a noncoherent DLL is affected not only by additive white Gaussian noise (AWGN) but also by multipath fading. This thesis investigates the behavior of noncoherent DDLs in a class of simple time-varying fading channels. Numerical method is used to solve the transition probability density function (pdf) of the tracking error and to study the transient behavior of a noncoherent loop. Detailed discussion on the numerical problems encountered in the course of deriving the desired solution is provided. {\it Mean time to lose lock} (MTLL) and {\it tracking error} are the two major performance measures of concern to us. Because the code phase error can be modeled as a renewal process, {\it Renewal Process Approach} (RPA) can be applied to analyze the performance of tracking loops. In a time-varying channel, however, we find that stationary analysis using RPA does not lead to correct estimates of the MTLL and the tracking error. We also analyze the performance of a class of code tracking loops called improved DLL that has a wider S-curve, larger pull-in and lock-in ranges.