調變信號之亂碼偵測與頻率同步

Abstract

先前關於頻率同步的研究大多集中在無調變的載波信號上。本論文將有系統的探討調變信號(modulated signals)在加成性白高斯雜訊(AWGN)通道及頻率非選擇性衰褪通道(frequency nonselective fading channel)的頻率同步。根據最大相似度(maximum likelihood, ML)原理我們可以得到最佳的固定頻率誤差之估計法則。如果考慮其近似的簡化函數，則我們可以得到複雜度較低的類似非同調結合(noncoherent combining)之頻率估計方法。另一方面我們也從廣義最大相似度(generalized maximum likelihood, GML)的原理來推導出同時估計頻率及信號或符元時間(symbol timing)的結構。 接下來我們研究了高動態環境下之頻率獲取與追蹤。我們根據最小平方差(least-squares)的原理所推導出的遞迴式估計，不但可以達到快速頻率獲取與追蹤，而且具有極小的均方差(mean squared frequency error)。我們也同時分析此項頻率獲取與追蹤系統的均方差。最後一個探討的問題為調變信號之亂碼偵測，我們利用其與頻率同步類似之特性及原理，得到了各種在符元同步及非同步情形下之檢測方式。 我們比較了各種頻率與亂碼檢測方式之錯誤偵測機率(outlier probability)或檢測操作特性(detector operating characteristic, DOC)效能，同時也提出一種廣義最大相似度檢測在硬體實現上較有效也較簡化的方法。

Frequency synchronization and code acquisition are two broad but well-established areas in communication theory. What we are interested here are two operating scenarios that have not been systematically investigated before. The first scenario occurs when no synchronization preamble (pilot channel or pilot symbols) is available and synchronization (or acquisition) has to be accomplished in the presence of data modulation. The second scenario we consider is a high-dynamic environment in which the carrier frequency undergoes very rapid variation. For the first scenario, we invoke the principles of maximum likelihood (ML) and generalized maximum likelihood (GML) to derive the estimates of the unknown parameters. We derive optimal (in the sense of Bayes or Neyman-Pearson) and suboptimal frequency estimates and code acquisition detectors with and without symbol timing information. A simple systematic means for their realization is also suggested. As for the second scenario, fast and real-time estimate is called for. Based on the relationship between the channel dynamic and the signal parameter(s), we adopt a model-based approach, modeling the received signal phase trajectory as a polynomial in $t$ (time) and solving for the coefficients whose associated model fits the received samples in the least-square (LS) sense. Certainly, the idea of LS fit is not new but we have succeeded in transforming the known batch-form solutions to recursive forms so that they can be applied for fast frequency acquisition and tracking. Furthermore, we are able to provide rigorous and complete mean-squared error analysis. For both scenarios, we consider both additive white Gaussian noise (AWGN) and Rician fading channels and present some related numerical examples of the performance of the resulting estimates or detectors.