在本論文裡我們探討多訊符相差偵測 (Multiple Symbol Differential Detection) 應用
於 DS-CDMA 系統之可行性，多訊符相差偵測在 AWGN 頻道為一種有效的非同
調解調方式，若考慮 MPSK調變器，此種方法所得到的性能比非常趨近同調檢
測，然而在 frequency-selective fading 中，探討其可行性之研究並不多，本論文
研究將多訊符序列偵測結合耙式接收器(Rake receiver)來做為信號的解調方法。
傳統上，耙式接收器有兩種的解調方式，一為同調檢測，另一為非同調檢測。
在同調的解調方式上，每一耙式接收器的路徑均須做頻道估測，優點為性能比
的提昇，缺點為複雜度與運算量的增加，相反的，在非同調的解調系統中，相
對於同調解調則是性能比的衰退與複雜度的簡化，我們建議了一種多訊符序列
偵測耙式接收器，針對一個 DS-CDMA 系統，我們進行電腦模擬研究，研究結
果顯示，若僅考慮硬判決之解碼器，耙式接收器的路徑越多與解調器的多訊符
決定區間越長，性能比將越好，這在傳統一個訊符的相差解調是不會發生的，
然而我們也發現此種方法在耙式接收器的路徑越多時，性能比與同調偵測差距
有加大之趨勢，因此，我們再利用Vietrbi的解調方式，來解differential的序列，
這種在多個狀態之後才做決定的方式將使我們的效能得到進一步的改善。

In this thesis, we take an application of multiple symbol differential detection (MSDD)
technique in direct-sequence code division multiple access (CDMA) system. It is well-
known that MSDD is an effective noncoherent demodulator which outperform the
conventional M-ary differential phase shift keying (MDPSK) in additive white Gaussian
noise (AWGN) channel. Take MPSK demodulator into consideration, the performance
of MSDD based on noncoherent demodulation approaches the performance of coherent
demodulation. However, there is little research about MSDD in frequency-selective
fading channel. We are now combining the MSDD and Rake receiver to be the signal
demodulator. In conventional, there are two kinds of Rake receivers. One is coherent
demodulator. Another is noncoherent demodulator. For coherent demodulation, it needs
to have channel estimation at each path. The advantage is that the performance will be
improved. On the other hand, the disadvantage is complexity and operation will increase.
On the contrast, for noncoherent demodulation, it is the performance degradation and
complexity simplification. In this thesis, We suggest a multiple symbol differential detection
on Rake receiver for CDMA system. From our computer simulation, only for hard decision,
the performance is improved and the improvement is proportional to the number of multipath
and the number of the length of multiple symbol. This will not happen in conventional MDPSK.
However, from our observation, the improvement of performance is degrading as the number
of multipath increase. Thus, we employee the technique of Viterbi decoding differential
detection (VDDD) to demodulate the differential sequence. By the property of decision
interval, the VDDD can obtain additional improvement.

Chapter 1 Introduction 1
Chapter 2 Conventional Communication System
2.1 Introduction 4
2.2 Convolutional Encoder and Decoder 6
2.2.1 The Convolutional Encoder 6
2.2.2 Decoding of Convolutional Code - Viterbi Algorithm 9
2.3 Interleaver / Deinterleaver 13
2.4 Spreading / Despreading 14
2.5 Channel Model 16
2.5.1 Doppler Shift 16
2.5.2 Characteristics of the Mobile Radio Channel 17
2.5.3 The Bello Functions 18
2.6 Rake Receiver 25
2.6.1 The Optimum Coherent Rake Receiver 28
2.6.2 Rake Receiver for Differential Modulation 32
Chapter 3 MSDD in Rake Receiver for DS/CDMA System
3.1 Introduction 36
3.2 Differentially Coherent Demodulation for Different BPSK 37
3.3 Multiple-Symbol Differential Detection 41
3.4 A New Approach to Apply MSDD in CDMA System 51
3.5 Viterbi-decoding differential detection of DPSK (VDDD) 57
3.5 Simulation Result 61
Chapter 4 Conclusions 67
References 68

[1]. Abrardo, G. Benelli, and G. Cau, "Multiple-symbol differential detection of
GMSK," Electronics Letters, Vol. 29. No. 25, pp. 2167-2168. 9th December
1993.
[2]. D. Divsalar and M. K. Simon, "Multiple trellis coded modulation (MTCM),"
JPL Publ. 86-44 (MSAT-X Rep. 141), Nov. 15, 1986. Also, IEEE Trans.
Commun., vol. 36, pp. 4310-419, Apr. 1988.
[3]. D. Divsalar, and M. K. Simon, "Multiple Symbol Differential Detection of
Uncoded and Trellis Coded MPSK," Technical Report, Jet Propulsion
Laboratory, JPL 89-38, November 1989.
[4]. D. Divsalar, M. K. Simon, and M. Shahshahani, "The performance of trellis
coded MDPSK with multiple symbol detection," IEEE Trans. Commun.,
vol. pp. 1391-1403, Sept. 1990.
[5]. D. Divsalar and M. K. Simon, "Multiple-symbol differential detection of
MPSK." IEEE Trans. Commun., Vol. 38. No. 3, pp. 300-308, March 1990.
[6]. D. Divsalar, M. K. Simon, and M. Shanshahani, "The performance of trellis-
coded MDPSK with multiple symbol detection." IEEE Trans. Commun.,
Vol. 38, No. 9, pp. 1391-1403, September 1990.
[7]. D. Divsalar and M. Simon, "Maximum-likelihood differential detection of
uncoded and trellis coded amplitude phase modulation over AWGN and
fading channels-Metrics and performance," IEEE Trans. On Commun.,
Vol. 42, No 1, Jan. 1994.
[8]. D. Makrakis, A. Yongancoglu, and K. Feher, "A Sequential Decoder for
Differentially Detection of Trellis Coded PSK Signals," Proc., IEEE
International Conference on Communications, pp. 1433-1438, June 1988.
[9]. D. Makrakis, and P. Mathiopoulos, "Optimal Decoding in Fading Channels:
A Combine Envelope, Multiple Differential and Coherent Detection Approach,
" Proc., IEEE Globecom89, Dallas, pp. 1551-1557, November 1989.
[10]. F. Adachi and M. Sawahashi, "Viterbi Decoding Differential Detection of
DPSK," Electronics Letters, vol. 28, no. 23, pp. 2196-2198, 5th Nov. 1992.
[11]. G. M. Vitetta and D. P. Taylor, "Maximum Likelihood Sequence Estimation
of Uncoded and Coded PSK Signals Transmitted over Rayleigh Flat-Fading
Channels," Conf. Rec. ICC`94, pp. 1-7, New Orleans, Louisiana, May 1994.
[12]. G. M. Vitetta and D. P. Taylor, "Viterbi decoding differentially encoded PSK
signals transmitted over Rayleigh frequency-flat fading channels," IEEE Trans.
Commun., vol. 43, pp. 1256-1259, Feb./Mar./Apr. 1995.
[13]. H. Leib and S. Pasupathy, "The phase of a vector perturbed by Gaussian noise
and differentially coherent receivers," IEEE Transaction on Information Theory,
Vol. 34, No. 6, pp. 1491-1501, November 1988.
[14]. H. Leib, "Data-aided noncoherent demodulation of DPSK," IEEE Trans.
Commun., vol. 43, pp. 722-725, Feb./Mar./Apr. 1995.
[15]. John David Parsons, The Mobile Radio Propagation Channel, Halsted Press, a
Division of John Wiley & Sons, New York, 1992.
[16]. J. Viterbi, "When not to spread spectrum-A sequel," IEEE Commun. Mag., vol.
23, no, 4, pp. 12-17, Apr. 1985.
[17]. J. Viterbi and J. K. Omura, Principles of Digital Communications and Coding.
Tokyo, Japan: McGraw-Hill, 1927.
[18]. J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1995.
[19]. J. Ventura-Traveset, G. Caire, E. Bilglieri, and G. Tarcco "Impact of diversity
reception on fading channels with coded modulation. Patt I: Coherent detection,
" submitted to IEEE Trans. On Commun., August 1995.
[20]. J. Liu, J. Kim, S. C. Kwatra and G. H. Stevens, "An analysis of the MPSK scheme
with differential recursive detection (DRD)," Proceedings of IEEE Conference
On Vehicle Technology '91, pp. 741-746,1991.
[21]. K. Yu and P. Ho, "Trellis Coded Modulation with Multiple Symbol Differential
Detection," Conf. Rec. ICC'93, pp. 1414-1418, Geneva, Switzerland, May 1993.
[22]. M. K. Simon and M. S. Alouini, "A unified approach to the probability of error
for noncoherent and differentially coherent modulations over generalized fading
channels," IEEE Trans. Commun., vol. COM-46, pp. 1625-1638, December 1998.
[23]. M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communication Techniques-
Signal Design and Detection, Englewood Cliffs, NJ: PTR Prentice Hall, 1995.
[24]. P. Ho and D. K. P. Fung, "Error performance of multiple symbol differential detection
of PSK signals transmitted over correlated Rayleigh fading channels," IEEE Trans
Commun., vol. 40, pp. 1566-1568, Oct. 1992.
[25]. P.E.H. Chow, and D.H.S. Ko, "Improving DCPSK Transmission by Means of Error
Control," IEEE Trans on Communications, October 1971.
[26]. P. Schramm, "Differentially coherent demodulation for differential BPSK in spread
spectrum systems," Vehicular Technology, IEEE Trans., vol. 48.5, pp. 1650-1656,
Sep. 1999.
[27]. Philip A. Bello, "Characterization of Randomly Time-Variant Linear Channels," IEEE
Transactions on Communications Systems, vol. CS-11, pp. 360-393, December 1963.
[28]. Raymond Steele (ed.), Mobile Radio Communications, Pentech Press, London, 1992.
[29]. S. G. Wilson, J. Freebersyser, and C. Marshall, "Multiple-symbol Detection of M-DPSK,
" Proceedings of IEEE GLOBECOM '89, Dallas, TX., pp. 1692-1697, Nov. 1989.
[30]. S. Haykin, Adaptive Filter Theory, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
[31]. W. C. Lindsey, and M. K. Simon, Telecommunication Systems Engineering, Prentice-
Hall, 1973.
[32]. W. Liu and P. Ho, "On multiple-symbol differential detection of PSK signals in frequency
selective fading channels." Unpublished manuscript, 1993.