應用於直接序列分碼多工系統中碼擷取之適應性濾波技術

Abstract

在直接序列分碼多工系統中，碼擷取是一個很重要的課題。傳統上，相關器常被用 來解決此問題。然而，其碼擷取的性能卻因多重使用者干擾而嚴重惡化。我們熟知 在接收機端架設陣列天線可以有效的壓制多重使用者干擾。但是，在多天線系統 下，大多數的碼擷取系統依舊是倚賴相關器。由於相關器固有的性質，使得基於相 關器所設計的碼擷取系統通常擁有較長的平均碼擷取時間。最近，適應性濾波技術 被應用於此問題上。儘管，此技術能提供較佳的碼擷取性能，但是它的計算複雜度 卻隨著延遲不確定性變大而增加。而且，在適應性多天線系統下，有效率的碼擷取 系統尚未被研究。在本論文中，我們發展新的適應性演算法來解決前述問題。 為了對付長延遲的問題，首先，我們提出了一個多率(multirate)碼擷取系統。它是由 多個不同碼擷取單元所組成的，而這些單元擁有不同的信號處理速率。拜多率信號 處理中抽取(decimation)性質之賜，整體的計算複雜度可以被大量降低。我們亦分析 了適應性濾波器的收斂以及平均碼擷取時間。由實驗結果可以看出，當多率碼擷取 系統與傳統適應性濾波碼擷取系統性能相近時，多率系統僅需非常低的計算複雜 度。 在適應性多天線系統下，我們提出的系統可以遠優於傳統上基於相關器所設計的系 統。提出的系統包含了兩個適應性濾波器，一個適應性空間濾波器與一個適應性時 間濾波器。經由特別的設計，空間濾波器可以作為波束成型器，而時間濾波器可以 作為碼延遲的估計器。基於最小均方差的準則，我們利用隨機梯度坡降法(stochastic gradient decent method)來同時調整這兩個濾波器。我們亦仔細的分析了其碼擷取性 能與收斂行為。由模擬結果可以看出: 提出系統的平均碼擷取時間遠低於傳統相關 器所設計的系統，以及理論的分析是正確的。 最後，我們設計了兩個演算法來優化前述的適應性多天線碼擷取系統。首先，在第 一個研究裡，我們藉由連續搜尋技術，可以大量的縮短時間濾波器的長度，同時可 以達到降低計算複雜度。我們對此低複雜度系統分析並得到相關的固定表示式。由 模擬結果，可以看出此系統可以藉由稍微犧牲性能以大量降低計算複雜度。此外， 我們發現在多路徑通道中，前述的適應性多天線碼擷取系統有收斂變慢的傾向。為 了解決收斂便慢的問題，在第二個研究裡，我們提出了一個基於共軛梯度法所設計 的適應性演算法。與傳統的共軛梯度法相比，所提出的方法是低計算複雜度的，這 是由於我們利用輸入信號的相關性矩陣中特殊結構。由模擬結果可以看出，與傳統 的共軛梯度法相比，所提出的低複雜度共軛梯度適應性演算法擁有相近的收斂速 度。

Code acquisition has been an important issue in direct-sequence/code-division multiple access (DS/CDMA) systems. The conventional solution to this problem is to use the correlator. However, the corresponding acquisition performance is significantly degraded when multiple access interference (MAI) is present. It is well-known that the receiver equipped with an antenna array can effectively suppress MAI. However, most code acquisition schemes for array systems still rely on the correlator structure. Due to the inherent property, the mean acquisition time of the correlator-based approaches is usually large. Recently, adaptive-filtering technique was applied to solve the problem. Although adaptive-filtering systems can provide better performance, its computational complexity becomes high when the delay uncertainty becomes large. Also, effective adaptive array systems for code acquisition have not been investigated yet. In this dissertation, we have developed novel adaptive algorithms solving the problems mentioned above. To cope with the large code delay problem, we first propose a multirate acquisition system, which is comprised of several acquisition units operating in different processing rates. Thanks to the decimation property in multirate processing, the overall computational complexity can be greatly reduced. Theoretical analysis of filter convergence and mean acquisition time is also provided. Experimental results show that while the proposed scheme can have comparable performance with respect to the conventional adaptive filtering scheme, its computational complexity is much lower. We then propose an adaptive array system having superior performance than the conventional correlator-based system. The proposed scheme comprises two adaptive filters, an adaptive spatial and an adaptive temporal filter. With a specially designed structure, the spatial filter can act as a beamformer suppressing interference, while the temporal filter can act as a code-delay estimator. A mean squared error (MSE) criterion is proposed such that these filters can be simultaneously adjusted by a stochastic gradient descent method. The performance as well as the convergence behavior of the proposed algorithm are analyzed in detail. Simulations show that the mean acquisition time of the proposed algorithm is much shorter than that of the correlator-based approach, and the derived theoretical expressions are accurate. Finally, we develop algorithms refining the proposed adaptive array acquisition system. The first approach is to incorporate a serial-search technique. By this way, we are able to significantly reduce the size of the temporal filter, so does the computational complexity. We also analyze the proposed low-complexity system and derive related closed-form expressions. Simulations show that while the refined system slightly compromises the performance, the computational complexity is much lower. In multipath-channel environments, the convergence of the proposed adaptive array system tends to be slow. In the second approach, we propose an adaptive algorithm with the conjugate gradient (CG) method to solve the problem. Unlike the original CG method, the proposed method, exploiting the special structure inherent in the input correlation matrix, requires a low computational-complexity. Simulation results show that the performance of adaptive array code acquisition with the proposed CG method is comparable to that with the original CG method.