串行级联CPM系统的迭代译码研究
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摘要
提高信息传输的可靠性和有效性，始终是通信领域研究与追求的目标。纠错编码是提高信息传输可靠性的一种重要手段。1948年，Shannon的开创性论文“通信的数学理论”为信道编码技术的发展指明了方向。现有军用通信系统的应用领域中，往往要求在恶劣的通信环境，比如移动、多径、动态变化等条件下仍能保持稳定的高速率数据通信，这就需要具有高功率效率和高频谱效率的编码调制体制与之相适应。
本文在研究Turbo码的基础上，主要对串行级联连续相位调制(SCCPM)系统的迭代译码进行了比较详细、深入的研究，系统地分析了SCCPM系统的性能。本文的研究内容主要有以下几个方面：
(1)探讨了Turbo码的编译码原理，包括并行级联卷积码(PCCC)与串行级联卷积码(SCCC)，对PCCC与SCCC的性能作了详细的分析，比较了两者的优缺点，分析了MAP、软输入软输出(SISO)等后验概率算法。
(2)研究了连续相位调制技术(CPM)的基本原理，给出了CPM信号的网格图描述，针对CPM内在的编码特性引入了CPM的分解模型，分析了分解模型的良好特性。
(3)本文有效地结合了Turbo码与连续相位调制技术，着重研究了SCCPM系统，对SCCPM系统的性能作了较为详细的分析，主要研究了交织长度、迭代次数、CPM的调制指数、关联长度、基带成形脉冲以及不同卷积码等参数对SCCPM系统性能的影响。
(4)系统分析了SCCPM系统的迭代译码的复杂度。引入了Laurent分解技术将非线性的CPM分解为一系列的PAM波形叠加的形式，利用Laurent分解的特性在保持性能的条件下给出了CPM的最佳接收机的简化模型。将Laurent分解的特性应用于SCCPM系统，理论分析可以有效地减少接收端匹配滤波器以及迭代译码网格状态的数目，明显地降低了SCCPM系统迭代译码的复杂度。
To improve the reliability and effectivity of information transmission is always the goal which we pursuit in the field of communication. Error correction coding is an important method to improve the reliability of information transmission.Shannon pointed out the direction for the channel coding technology in his famous thesis on "A mathematical theory of communication" in 1948. In the existing military communication systems,we should achieve stable and high speed data communications in poor communication environment, such as mobile, multi-path, and dynamic etc., which require coding and modulation systems with high efficiency of power and spectrum correspondingly.
In this thesis, Serially Concatenated Continuous Phase Modulation(SCCPM) system is studied in detail. The SCCPM system is based on Turbo code and Continuous Phase Modulation technology. Performance of the SCCPM system is analyzed particularly.The main content of this thesis as follows:
(1) The coding and iterative decoding principle of Turbo code (PCCC) and Serial Concatenated Convolutional Codes (SCCC) are studyed. Enough simulations on PCCC andSCCC in MATLAB is given. The difference between SCCC and ?CCC on performance is studied.The posterior probability algorithms (MAP,SISOetc.) are also derived in detail.
(2) The principle of CPM is studied.The CPM signal is described on trellis. Given the inherent memory of CPM, decomposition module is introduced in this thesis.The outstanding performance of the decomposition module is also analyzed.
(3) The SCCPM system is based on Turbo code and CPM. Performance of the SCCPM system is analyzed detailedly. Also a more detailed analysis on parameters,such as: iterleaver length,iterative number,modulation index of CPM, correlative length of CPM, baseband impulse of CPM and convolutional code'generator matrix etd,which affect the performance of the SCCPM system is given.
(4) The complexity of iterative decoding of the SCCPM system is analyzed in detail. The CPM signal can be expressed as a sum of finite number of time limited amplitude modulation pulses by Laurent Decomposition. The optimum receiver of CPM is simplified by Laurent Decomposition. In theory, the numbers of matched filter and trellis state can be redeced apparently by Laurent Decomposition.So, the complexity of iterative decoding of the SCCPM system can be reduced by using the property of Laurent Decomposition.
本文在研究Turbo码的基础上，主要对串行级联连续相位调制(SCCPM)系统的迭代译码进行了比较详细、深入的研究，系统地分析了SCCPM系统的性能。本文的研究内容主要有以下几个方面：
(1)探讨了Turbo码的编译码原理，包括并行级联卷积码(PCCC)与串行级联卷积码(SCCC)，对PCCC与SCCC的性能作了详细的分析，比较了两者的优缺点，分析了MAP、软输入软输出(SISO)等后验概率算法。
(2)研究了连续相位调制技术(CPM)的基本原理，给出了CPM信号的网格图描述，针对CPM内在的编码特性引入了CPM的分解模型，分析了分解模型的良好特性。
(3)本文有效地结合了Turbo码与连续相位调制技术，着重研究了SCCPM系统，对SCCPM系统的性能作了较为详细的分析，主要研究了交织长度、迭代次数、CPM的调制指数、关联长度、基带成形脉冲以及不同卷积码等参数对SCCPM系统性能的影响。
(4)系统分析了SCCPM系统的迭代译码的复杂度。引入了Laurent分解技术将非线性的CPM分解为一系列的PAM波形叠加的形式，利用Laurent分解的特性在保持性能的条件下给出了CPM的最佳接收机的简化模型。将Laurent分解的特性应用于SCCPM系统，理论分析可以有效地减少接收端匹配滤波器以及迭代译码网格状态的数目，明显地降低了SCCPM系统迭代译码的复杂度。
To improve the reliability and effectivity of information transmission is always the goal which we pursuit in the field of communication. Error correction coding is an important method to improve the reliability of information transmission.Shannon pointed out the direction for the channel coding technology in his famous thesis on "A mathematical theory of communication" in 1948. In the existing military communication systems,we should achieve stable and high speed data communications in poor communication environment, such as mobile, multi-path, and dynamic etc., which require coding and modulation systems with high efficiency of power and spectrum correspondingly.
In this thesis, Serially Concatenated Continuous Phase Modulation(SCCPM) system is studied in detail. The SCCPM system is based on Turbo code and Continuous Phase Modulation technology. Performance of the SCCPM system is analyzed particularly.The main content of this thesis as follows:
(1) The coding and iterative decoding principle of Turbo code (PCCC) and Serial Concatenated Convolutional Codes (SCCC) are studyed. Enough simulations on PCCC andSCCC in MATLAB is given. The difference between SCCC and ?CCC on performance is studied.The posterior probability algorithms (MAP,SISOetc.) are also derived in detail.
(2) The principle of CPM is studied.The CPM signal is described on trellis. Given the inherent memory of CPM, decomposition module is introduced in this thesis.The outstanding performance of the decomposition module is also analyzed.
(3) The SCCPM system is based on Turbo code and CPM. Performance of the SCCPM system is analyzed detailedly. Also a more detailed analysis on parameters,such as: iterleaver length,iterative number,modulation index of CPM, correlative length of CPM, baseband impulse of CPM and convolutional code'generator matrix etd,which affect the performance of the SCCPM system is given.
(4) The complexity of iterative decoding of the SCCPM system is analyzed in detail. The CPM signal can be expressed as a sum of finite number of time limited amplitude modulation pulses by Laurent Decomposition. The optimum receiver of CPM is simplified by Laurent Decomposition. In theory, the numbers of matched filter and trellis state can be redeced apparently by Laurent Decomposition.So, the complexity of iterative decoding of the SCCPM system can be reduced by using the property of Laurent Decomposition.
引文
[1] Shannon C E. A Mathematical Theory of Communication. The Bell System Technical Journal. 1948,27:623-656.
[2] Berrou C, Glavieux A, Thitimajshima P. Near Shannon limit error-correcting coding coding and decoding:Turbo-codes(1).Proc. ICC 93. Geneva, Switerland. 1993:1064-1074.
[3] Berrou C, Glavieux A. Near optimum error correcting coding and decoding:Turbo-codes. IEEE Trans. Comm. 1996, 44(10):1261-1271.
[4] Benedetto S,Dicsalar D,Montorsi G. Serial concatenation interleaved codes: performance analysis, dedign and iterative decoding. TDA Progress Report 42-126.1996,8:1-26.
[5] Benedetto S, Dicsalar D, Montorsi G. A soft-input soft-output maximum a posteriori (MAP) module to decode parallel and serial concatenated codes. TDA Progress Report 42-127.1996,12:1-20.
[6] Benedetto S, Dicsalar D, Montorsi G. Soft-output decoding algorithms in iterative decoding of Turbo codes. TDA Progress Report 42-124.1998,2:63-87.
[7] Anderson J B, Aulin T, Sundberg C E. Digital Phase Modulation. Plenum Press, NY. 1986.
[8] Aulin T, sundberg C E W. Continuous phase modulation-Part I:Full response signaling. IEEE Trans. Comm. 1981, 29:196-209.
[9] Aulin T, Rydbeck N, sundberg C E W. Continuous phase modulation-Part II:Partial response signaling. IEEE Trans. Comm. 1981, 29:210-225.
[10] Pizzi S V, Wilson S G.Convolutional coding combined with continuous plase modulation. IEEE Trans. Comm. 1985,29:20-29.
[11] Lindell G. On Coded continuous phase modulation:Ph. D. Thesis, Dept. of Telecomm. Theory, Univ. of Lund, Sweden, 1985.
[12] Morales-Moreno F, pasupathy S. Structure, optimization snd realization of FFSK trellis codes. IEEE Trans. Inf. Theory. 1998, 34:730-741.
[13] Huber J, Liu W. An alternative approach to reduced-complexity CPM-receivers. IEEE Journal on Sel. Areas in Comm. 1989, 7:1437-1449.
[14] Morales_Moreno F, Holubowicz W, Pasupathy S. Optimization of trellis coded TFM via matched codes. IEEE Trans. Comm. 1994,42:1586-1594.
[15] Yang R H -H, Taylor D P. Trellis-coded continuous-phase frequency-shift keying with ring convolutional codes. IEEE Trans. Inf. Theory. 1994,40:1057-1067.
[16] Massey J L, Mittelholzer T. Convolutional codes over rings. Proc. 4th Joint Swedish-Soviet Int. Workshop on Inf. Theory. Gotland, Sweden. 1989:14-18.
[17] Rimoldi B,Li Q. Coded continous phase modulation using ring convolutinal codes. IEEE Trans. Comm. 1995, 43:2714-2720.
[18] Moqvist P, Aulin T M. Serially concatenated continuous phase modulation whth iterative decoding. IEEE Trans. Comm. 2001, 49(11):1901-1915.
[19] Narayanan K R, Stuber G L. Performance of trellis-coded CPM with iterative demodulation and decoding. IEEE Trans. Comm. 2001, 49:676-687.
[20] Moqvist P, Aulin T. Power and bandwidth efficient serially concatenated CPM with iterative decoding. Proc. IEEE GLOBECOM' 00.2000:790-794.
[21] Svenssion A, Aulin T, Sundberg C E W. A chass of reduced complexity Viterbi detectors for partial response continuous phase modulation. IEEE Trans. comm. 1983,32:1079-1087.
[22] Svenssion A. Reduced state sequence detection of partial response continuous phase modulation. Proc. lnst. Elec. Eng. 1991, 138(4):256-268.
[23] Simmons S J, Wittke P H. Low complexity decoders for constant envelope digital modulationis. IEEE Trans. comm. 1983, 31:1273-1280.
[24] Kaleh K G. Simple coherent receivers for partial response continuous phase modulation. IEEE J. Selected Areas Comm. 1989, 7:1427-1436.
[25] Palenius T, Svenssion. Reduced complexity detectors for continuous phase modulation based on a signal space approach. European Trans. Telecommun. 1993, 4(3):51-63.
[26] Chen X P, Chugg K M. Reduced-state soft-input/soft-output algorithms for complexity redection in iterative and non-iterative data detection. IEEE Int Conf Commun(ICC' 00). New Orleans. 2000, 3:6-10.
[27] Chen X P, Chugg K M, Heo J. Reduced state adaptive SISO algorithms for serially concatenated CPM over frequency-selective fading channels. IEEE Global Telecomm Conf. San Antonio. 2001, 3:1162-1666.
[28] Chung K, Heo J. RS-A-SISO algorithms for serially concatenated CPM over fading channels and density evolution analysis. Electron Lett. 2003, 22(39):1597-1598.
[29] Sun Jinhua, Li Jiandong, Jin Lijun. A RS-SISO algorithm for serially concatenated continuous phase modulation. AINA. 2005, 1:941-946.
[30] 刘东华．Turbo码原理与应用技术．北京：电子工业出版社，2004：第三章．
[31] 韩志学．连续相位调制短波瞬间通信系统关键技术研究：(博士学位论文)．哈尔滨：哈尔滨工程大学，2007．
[32] Rimoldi B. A decomposition approach to CPM. IEEE Trans. Inf. Theory. 1988, 34:260-270.
[33] Gallager R G. Low-Density Parity-Check Codes. IRE. Trans. Inform. Theory. 1962, 8:21-28.
[34] Forney G D, Jr. Concatenated codes. M. I. T. Press. Cambridge, MA, USA. 1966.
[35] Bahl L R, Cocke J, Jelinek F, Raviv J. Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inf. Theory. 1974, 20:284-287.
[36] 王新梅，肖国镇．纠错码-原理与方法．西安：西安电子科技大学，1991．
[37] Li Y, Vucetic B, Sato Y. Optimum soft-output detection for channels with intersymbol interference. IEEE Trans. Inf. Theory. 1995, 41:704-713.
[38] Moqvist P. Serially concatenated systems:An iterative decoding approach with application to continuous phase modulation. Lic. Eng. Thesis. Dept. of Comp. Eng. Chalmers Univ. of Techn. Goteborg, Sweden. 1999.
[39] Gronemeyer S A, McBride A L. MSK and offset QPSK modulation. IEEE Trans. Commun. 1976, 24:809-820.
[40] Amoroso F, Kivett J A. Simplified MSK signaling technique. IEEE Trans. Commun. 1977, 25: 433-441.
[41] Pasupathy S. Minimum shift keying:A spectrally efficient modulation. IEEE Trans. Commun. Mag. 1979, 17:14-22.
[42] Laurent P A. Exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses(AMP). IEEE Trans. comm. 1986, 34(2):150-160.
[43] Mengali U, Morelli M. Decomposition of M-ary CPM signals into PAM waveforms. IEEE Trans. Inf. Theory. 1995, 41(5):1265-1275.
[44] Shane M R, Wesel R D. Reduced Complexity Iterative Demodulation and Decoding of Serial Concatenated Continuous Phase Modulation. IEEE Ice' 02. 2002, 3:1672-1676.
[45] Perrins E, Rice M. PAM decomposition of M-ary Multi-h CPM. IEEE Trans. Comm. 2005, 53(12): 2065-2075.
[46] Benedetto S, Montorsi G. Unveiling Turbo codes:some results on parallel concatenated coding schemes. IEEE Trans. Inf. Theory. 1996, 42:409-428.
[47] Brink S. Convergence of iterative decoding. Electronics Letters. 1999, 35(13):1117-1119.
[48] Wu Yufei. Implementation of parallel and serial concatenated convolutional codes. Doctor Thesis of Virginia Polytechnic Institute and State University. 2000.
[49] 彭翔．跳频环境下CPM同步算法的研究：(硕士学位论文)．北京：中国科学院声学研究所，2004．
[50] 黄建忠．基于连续相位调制的串行级联系统：(硕士学位论文)．西安：西安电子科技大学，2006．
[2] Berrou C, Glavieux A, Thitimajshima P. Near Shannon limit error-correcting coding coding and decoding:Turbo-codes(1).Proc. ICC 93. Geneva, Switerland. 1993:1064-1074.
[3] Berrou C, Glavieux A. Near optimum error correcting coding and decoding:Turbo-codes. IEEE Trans. Comm. 1996, 44(10):1261-1271.
[4] Benedetto S,Dicsalar D,Montorsi G. Serial concatenation interleaved codes: performance analysis, dedign and iterative decoding. TDA Progress Report 42-126.1996,8:1-26.
[5] Benedetto S, Dicsalar D, Montorsi G. A soft-input soft-output maximum a posteriori (MAP) module to decode parallel and serial concatenated codes. TDA Progress Report 42-127.1996,12:1-20.
[6] Benedetto S, Dicsalar D, Montorsi G. Soft-output decoding algorithms in iterative decoding of Turbo codes. TDA Progress Report 42-124.1998,2:63-87.
[7] Anderson J B, Aulin T, Sundberg C E. Digital Phase Modulation. Plenum Press, NY. 1986.
[8] Aulin T, sundberg C E W. Continuous phase modulation-Part I:Full response signaling. IEEE Trans. Comm. 1981, 29:196-209.
[9] Aulin T, Rydbeck N, sundberg C E W. Continuous phase modulation-Part II:Partial response signaling. IEEE Trans. Comm. 1981, 29:210-225.
[10] Pizzi S V, Wilson S G.Convolutional coding combined with continuous plase modulation. IEEE Trans. Comm. 1985,29:20-29.
[11] Lindell G. On Coded continuous phase modulation:Ph. D. Thesis, Dept. of Telecomm. Theory, Univ. of Lund, Sweden, 1985.
[12] Morales-Moreno F, pasupathy S. Structure, optimization snd realization of FFSK trellis codes. IEEE Trans. Inf. Theory. 1998, 34:730-741.
[13] Huber J, Liu W. An alternative approach to reduced-complexity CPM-receivers. IEEE Journal on Sel. Areas in Comm. 1989, 7:1437-1449.
[14] Morales_Moreno F, Holubowicz W, Pasupathy S. Optimization of trellis coded TFM via matched codes. IEEE Trans. Comm. 1994,42:1586-1594.
[15] Yang R H -H, Taylor D P. Trellis-coded continuous-phase frequency-shift keying with ring convolutional codes. IEEE Trans. Inf. Theory. 1994,40:1057-1067.
[16] Massey J L, Mittelholzer T. Convolutional codes over rings. Proc. 4th Joint Swedish-Soviet Int. Workshop on Inf. Theory. Gotland, Sweden. 1989:14-18.
[17] Rimoldi B,Li Q. Coded continous phase modulation using ring convolutinal codes. IEEE Trans. Comm. 1995, 43:2714-2720.
[18] Moqvist P, Aulin T M. Serially concatenated continuous phase modulation whth iterative decoding. IEEE Trans. Comm. 2001, 49(11):1901-1915.
[19] Narayanan K R, Stuber G L. Performance of trellis-coded CPM with iterative demodulation and decoding. IEEE Trans. Comm. 2001, 49:676-687.
[20] Moqvist P, Aulin T. Power and bandwidth efficient serially concatenated CPM with iterative decoding. Proc. IEEE GLOBECOM' 00.2000:790-794.
[21] Svenssion A, Aulin T, Sundberg C E W. A chass of reduced complexity Viterbi detectors for partial response continuous phase modulation. IEEE Trans. comm. 1983,32:1079-1087.
[22] Svenssion A. Reduced state sequence detection of partial response continuous phase modulation. Proc. lnst. Elec. Eng. 1991, 138(4):256-268.
[23] Simmons S J, Wittke P H. Low complexity decoders for constant envelope digital modulationis. IEEE Trans. comm. 1983, 31:1273-1280.
[24] Kaleh K G. Simple coherent receivers for partial response continuous phase modulation. IEEE J. Selected Areas Comm. 1989, 7:1427-1436.
[25] Palenius T, Svenssion. Reduced complexity detectors for continuous phase modulation based on a signal space approach. European Trans. Telecommun. 1993, 4(3):51-63.
[26] Chen X P, Chugg K M. Reduced-state soft-input/soft-output algorithms for complexity redection in iterative and non-iterative data detection. IEEE Int Conf Commun(ICC' 00). New Orleans. 2000, 3:6-10.
[27] Chen X P, Chugg K M, Heo J. Reduced state adaptive SISO algorithms for serially concatenated CPM over frequency-selective fading channels. IEEE Global Telecomm Conf. San Antonio. 2001, 3:1162-1666.
[28] Chung K, Heo J. RS-A-SISO algorithms for serially concatenated CPM over fading channels and density evolution analysis. Electron Lett. 2003, 22(39):1597-1598.
[29] Sun Jinhua, Li Jiandong, Jin Lijun. A RS-SISO algorithm for serially concatenated continuous phase modulation. AINA. 2005, 1:941-946.
[30] 刘东华．Turbo码原理与应用技术．北京：电子工业出版社，2004：第三章．
[31] 韩志学．连续相位调制短波瞬间通信系统关键技术研究：(博士学位论文)．哈尔滨：哈尔滨工程大学，2007．
[32] Rimoldi B. A decomposition approach to CPM. IEEE Trans. Inf. Theory. 1988, 34:260-270.
[33] Gallager R G. Low-Density Parity-Check Codes. IRE. Trans. Inform. Theory. 1962, 8:21-28.
[34] Forney G D, Jr. Concatenated codes. M. I. T. Press. Cambridge, MA, USA. 1966.
[35] Bahl L R, Cocke J, Jelinek F, Raviv J. Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inf. Theory. 1974, 20:284-287.
[36] 王新梅，肖国镇．纠错码-原理与方法．西安：西安电子科技大学，1991．
[37] Li Y, Vucetic B, Sato Y. Optimum soft-output detection for channels with intersymbol interference. IEEE Trans. Inf. Theory. 1995, 41:704-713.
[38] Moqvist P. Serially concatenated systems:An iterative decoding approach with application to continuous phase modulation. Lic. Eng. Thesis. Dept. of Comp. Eng. Chalmers Univ. of Techn. Goteborg, Sweden. 1999.
[39] Gronemeyer S A, McBride A L. MSK and offset QPSK modulation. IEEE Trans. Commun. 1976, 24:809-820.
[40] Amoroso F, Kivett J A. Simplified MSK signaling technique. IEEE Trans. Commun. 1977, 25: 433-441.
[41] Pasupathy S. Minimum shift keying:A spectrally efficient modulation. IEEE Trans. Commun. Mag. 1979, 17:14-22.
[42] Laurent P A. Exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses(AMP). IEEE Trans. comm. 1986, 34(2):150-160.
[43] Mengali U, Morelli M. Decomposition of M-ary CPM signals into PAM waveforms. IEEE Trans. Inf. Theory. 1995, 41(5):1265-1275.
[44] Shane M R, Wesel R D. Reduced Complexity Iterative Demodulation and Decoding of Serial Concatenated Continuous Phase Modulation. IEEE Ice' 02. 2002, 3:1672-1676.
[45] Perrins E, Rice M. PAM decomposition of M-ary Multi-h CPM. IEEE Trans. Comm. 2005, 53(12): 2065-2075.
[46] Benedetto S, Montorsi G. Unveiling Turbo codes:some results on parallel concatenated coding schemes. IEEE Trans. Inf. Theory. 1996, 42:409-428.
[47] Brink S. Convergence of iterative decoding. Electronics Letters. 1999, 35(13):1117-1119.
[48] Wu Yufei. Implementation of parallel and serial concatenated convolutional codes. Doctor Thesis of Virginia Polytechnic Institute and State University. 2000.
[49] 彭翔．跳频环境下CPM同步算法的研究：(硕士学位论文)．北京：中国科学院声学研究所，2004．
[50] 黄建忠．基于连续相位调制的串行级联系统：(硕士学位论文)．西安：西安电子科技大学，2006．