混沌碼在直接序列展頻通訊系統之應用

Implementation of Chaotic Sequences on Direct-Sequence Spread-Spectrum System

謝春風(Chung-Feng Hsieh)

指導教授 ： 涂世雄

中原大學/工學院/電機工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500765

摘要

在本論文中，我們闡述混沌序列(chaotic sequences)在數位通訊上的應用。為了產生混沌序列，本文以簡單且被廣泛研究的非線性動態系統 logistic map 及 Tent map，以它為混沌序列的生成函數，由兩者所產生的序列，與普遍被使用的 M碼、Gold碼，利用互斥的原理，來形成新的二進制混沌序列，在展頻碼的應用上，其序列間的相關性(correlation)函數值是最佳的，非常適用於較大長度的展頻碼及較大數量使用者的環境下。
混沌序列的產生，Logistic map 由初始值作控制，而 Tent map 則控制其中變數，適當選取控制值，使其產生不同的混沌序列，其值皆在 {-1,1}中，不同使用者給予不同的控制值，產生不同的混沌序列配合不同使用者；所產生的序列，依照中間值判定準則，轉換為二進制碼，再分別與傳統的M碼、Gold碼，執行邏輯XOR動作，產生新的二進制混沌序列: 混沌碼、混沌與M碼組合和混沌與Gold碼組合；評估在不同展頻碼長度及不同數量使用者，在AWGN環境下的效能。混沌序列極易產生，且具有隨機特性、足夠長度、不可預測性大量的隨意數值等特性；用於通訊方面，可符合不同頻帶的展頻碼長度及任意數量的使用者，且其位元錯誤率(BER)效能優於傳統的展頻碼；使用者數量增加，效能愈偏好；展頻碼長度增加，效能愈改善，比傳統展頻碼更佳適用於多使用者通訊系統。

關鍵字

混沌碼 ； 直接序列 ； 展頻通訊

並列摘要

The thesis proposes the use of chaotic sequences combined with conventional code to generate chaotic spreading code for Direct- Sequence Spread-Spectrum (DSSS) systems. Using digitalization to utilize exploitable chaotic maps on the interval {-1, 1} with Logistic and Tent maps. Further, the chaotic sequences are reconstructed with conventional M-sequence or Gold sequences to form one of that a compound change into chaotic spreading code with logical XOR operator. Thus, the correlation performance of the chaotic spreading code is the objective optimized, which becomes better than the conventional sequences, the more number of users and large lengths of spreading factor is more advantageous than lower number of users and short lengths code.
The chaotic spreading codes utilize extractable extended large range of parameters for chaotic behavior which are well-known Logistic and Tent map. The chaotic sequences of both the Logistic sequences (produced by different initial condition) and the Tent sequences (generated by different parameters) are discoverable on limitation {-1, 1} range. For generation of the chaotic binary, the digitalization is used to distinguish by mean value. Next, both chaotic sequences are combined to form one with either classical M sequences or Gold sequences in executing XOR function to generate a new chaotic spreading code. There are definitely three types for design purposes: chaotic spreading code, chaos with M sequences and chaos with Gold sequence, that are used to evaluate performance under different conditions including number of users and lengths of spreading factor in AWGN environment.
Chaotic spreading codes can be easily produced for any number of users and allocated bandwidth by assigned code lengths. Moreover, no limitation and damage on the number of users and on required spreading factor. The bit error rate (BER) performance of the chaotic spreading code becomes better than the classical sequences, which the number of users increases as the performance is incremented. As well, as spreading factor increases the BER is improved. The system based on chaotic spreading code performs generally more than the conventional ones. Therefore, the chaotic spreading code used in multiple-access communication is reasonable.

並列關鍵字

Spread Spectrum ； Chaotic Sequences ； Direct Sequence

參考文獻

〔13〕 郭啟源, “A Chaostic Pseudo Random Number Generator,” 中原大學電機工程學系92學年度碩士論文.

〔17〕 G´eza Kolumb´an, Michael Peter Kennedy and Leon O. Chua, “The Role of Synchronization in Digital Communications Using Chaos—Part III: Performance Bounds for Correlation receivers,” IEEE Transactions on Circuits and Systems—I: fundamental theory and applications, vol. 47, no. 12, pp.1673-1683, December 2000.

〔5〕 Wesel Ellen Kayata, Wireless Multimedia Communications, Networking Video, Voice, and Data, Addison-Wesley, 2’nd. Jan. 1998.

〔6〕 Liru Lu and V. K. Dubey, “Complete Complementary Code for Spread Time CDMA System,” ISSSTA 2004. Sydney, Australia, 30 Aug. - 2 Sep. 2004.

〔7〕 Rethnakaran Pulikkoonattu and Markus Antweiler, “Analysis of Differential Non Coherent Detection Scheme for CDMA Pseudo Random (PN) Code Acquisition,” ISSSTA 2004, Sydney, Australia, 30 Aug. - 2 Sep. 2004.