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Wavelet Based CDMA and Its Performance Analysis
由母小波函數與子小波函數(daughter wavelet)組成的正交基(orthogonal basis)中的每個函數相互正交，小波函數的正交特性已成功的應用於多用戶通訊系統中。在本論文中我們首先以子小波作為用戶碼組傳送二元訊號，並搜尋在非同步情形下適用於多用戶系統的碼組。接著我們將適當組合數個子小波函數構成固定長度的wavelet packet based CDMA code，並搜尋出系統用戶之間相關性較小的碼組及適用於雙資訊傳輸率系統的dual chip rate wavelet packet based code作為用戶碼，並使用搜尋得到的碼組於多路徑衰減通道中傳遞訊號，利用statistic correlation distribution convolution(SCDC)方法分析系統於多路徑衰減通道環境的性能，在分析系統性能時，在接收端採用傳統接收機、Equal Gain Combining RAKE及Maximal Ratio Combining RAKE receiver三種類型的接收機，分析碼組在各種模式下的系統性能。我們也將比較wavelet packet based CDMA code與Gold code、m-sequence性能的差異。
小波函數具有良好的頻率-時間雙重解析度，如果系統能組合適當的碼組作為用戶碼，當訊號經過多路徑衰減通道後，在接收端處對訊號作判決及提高系統性能是很有幫助的。我們將在本實驗中證明：選用由較多層數所組成的節點wavelet packet based CDMA code應用於多路徑衰減通道中，具有較佳的frequency diversity性質，該碼組用於多重路徑通道中具有抗頻率選擇性衰減的特性。因此我們可以根據所測得的通道參數及其特性，組合適當節點的碼組，使該碼組訊號能在時域及頻域都能有良好的正交性質，克服通道所引起的多重路徑干擾，進而提高系統性能。
另外，實驗結果也顯示：在碼長度相同的四用戶及八用戶系統下，Haar wavelet packet based CDMA code之系統誤碼率比Gold code低，而且wavelet packet based CDMA code適合使用於dual chip rate CDMA system作為用戶碼。當wavelet packet code使用於多路徑衰減通道，對克服頻率選擇性衰減效應是很有用的。小波函數不同於一般傳統的Gold code、m-sequence等二元訊號所組成的展頻碼，小波函數是多值函數(multi-value)。小波函數所組成的碼組頻寬較小，比二元訊號所組成的展頻碼有較高的頻譜效益。
In this thesis, the feasibility of wavelet-based CDMA multiuser communication system is studied. In Chapter 2 of this thesis, as an initial effort to study the wavelet-based CDMA system, selection of wavelet functions for wavelet-based CDMA systems is carried out. In the selection process, we search the codes based only on their low cross-correlation levels (LCCLs). The found CDMA code sets are to be used in single chip rate CDMA systems. Chapter 3 is concentrated on study of wavelet-packet based CDMA systems for both single and dual chip rates systems. Suitable wavelet-packet functions are searched based on their low LCCLs. In Chapters 4, a numerical method, the statistic correlation distribution convolution (SCDC) algorithm, is developed to explicitly study bit error rate of wavelet-packet based CDMA systems under varying multipath fading environment. The performance of wavelet-packet based CDMA system is compared with that of traditional CDMA systems using Gold codes and m-sequences. Two different types of RAKE receiver structures, equal gain combining RAKE and maximum ratio combining RAKE, are also considered for the wavelet-packet based CDMA systems to mitigate multipath fading effects of mobile channels. Due to their two-fold resolution capability (time-frequency duel-resolution), the wavelet-packet functions can outperform traditional CDMA codes, such as Gold codes or m-sequences, under multipath-impaired channels. The reason for that is own mainly to the frequency diversity capability inherent to the wavelet-packet functions. The obtained results in Chapter 4 also show that Haar wavelet-packet based CDMA systems with four/eight users perform better than those using Gold codes of the same length, and wavelet-packet based CDMA codes are also suitable for dual chip rate systems. The another major advantage for using wavelet-packet based CDMA codes is that they occupy much narrower bandwidth than that of the ordinary binary codes, such as Gold codes or m-sequences. Therefore, they can provide a higher bandwidth efficiency. However, unlike tradition binary CDMA codes (as Gold code, m-sequence), the wavelet-packet based CDMA codes are multi-valued functions. Therefore, they require multi-level modulations in transmitters. Finally, the conclusion and remaining work are given in Chapter 5.
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