无线通信中迭代干扰抑制技术研究
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摘要
在当今日趋恶劣的电子战环境中,能够有效地抑制人为干扰是掌握战场主动权的关键,也是军事通信系统的重要研究目标。迭代检测作为一种很有吸引力的方案,已经在Turbo码、信道估计、多用户检测等领域得到了广泛的应用。在抑制人为干扰方面,迭代检测通过交换各个软输入软输出(Soft Input Soft Output,SISO)模块之间的外信息,通过迭代来逼近整个系统的最优解输出,使系统获得优越的抗干扰性能;迭代干扰估计在干扰类型已知的前提下,可以估计出干扰信号的特征参量或者干扰状态信息(Jamming State Information,JSI),并利用这些信息进一步优化迭代检测,提高系统的抗干扰能力。
另一方面,传统的跳频(Frequency Hopping,FH)技术具有较强的抗多径能力、抗人为干扰能力,如果把跳频通信系统与迭代检测技术结合在一起,则系统的综合性能指标,包括通信可靠性,保密性能,频谱利用率都会得到很大提升。因此,本文把跳频系统和连续相位调制(Continuous Phase Modulation,CPM)结合在一起,并研究了相应的迭代干扰抑制算法。
第二章简要介绍了迭代检测的原理与应用,并且建立了FH-CPM系统模型。CPM信号是一种有记忆非线性调制方式,通过CPM信号和信道码的串联形成具有类似串行级联卷积的信号结构,并在接收端进行联合解调译码迭代检测。CPM信号还有其他一些特点:它的信号能量集中,占用带宽小,对邻道的干扰小;是一种非线性调制,具有恒包络,可以使用效率更高的非线性放大器,而且其恒模特性还方便接收机进行信道估计。
第三章研究了相干FH-CPM迭代干扰抑制算法及其性能。并针对部分响应CPM信号解调复杂度高的问题,通过引入CPM信号的罗伦特分解,改进了软输入软数出解调算法,降低了接收机复杂度。在系统性能分析方面,由于迭代系统中交织器的引入,软输入软输出模块外信息的概率密度函数非常复杂,难以从数学上进行完备和准确的推导,因此采用了外信息转移图(Extrinsic InformationTransmission Chart,EXIT)进行了迭代收敛性的分析。仿真结果显示,这种系统方案和迭代检测算法在加性高斯白噪声(Additive White Gaussian Noise,AWGN)信道下有很好的误码率性能,在部分带干扰和多音干扰环境下也有较好的干扰抑制作用。
第四章研究了非相干FH-CPM迭代干扰抑制算法及其性能。提出了一种基于CPM信号罗伦特分解的迭代树搜索软输入软输出解调算法,并利用EXIT图分析了接收机的收敛特性。仿真结果显示,在迭代检测接收机中,跳内符号数为20时,采用非相干解调与相干解调的系统在加性高斯信道下所对应的误码率性能差距在1.5dB左右。
第五章研究了部分带干扰JSI估计算法,提出了一种多音干扰的JSI迭代估计算法。为了进一步提高系统的干扰抑制能力,文章考虑对接收信号进行迭代估计并把干扰状态信息输送给迭代检测器。针对部分带干扰,文章从干扰状态信息的后验概率出发,阐述了部分带干扰状态信息的迭代估计算法,并与迭代检测系统一起进行部分带干扰的抑制。仿真结果表明,迭代干扰估计器的引入,使得相干迭代干扰抑制在目标误码率10~(-4)处产生了接近3dB的性能增益:使得非相干迭代干扰抑制在目标误码率10~(-4)处产生了1dB的性能增益。针对多音干扰,本文提出了一种时域迭代估计算法,该算法能够通过迭代对干扰状态信息和干扰判决门限进行更新,避免了采用频域估计时干扰判决门限依靠经验值进行设定的缺点。仿真结果表明在原有迭代检测器的基础上,迭代干扰估计器的引入能够基本使得多音干扰信号被重建进而抵消,大大地改善了接收机的抗干扰性能。
In the severe interference environment of electronic warfare, it is important to suppress interference for reliability of systems. Iterative detection is an effective and promising signal processing method. The a prior information and the extrinsic information can be exchanged between soft-in soft -out (SISO) blocks, so that the optimal detection can be approached by introducing iterative detection. Moreover, jamming state information (JSI) can be calculated by iterative estimation. Combining the estimator and detector together, the receiver can greatly suppress the jamming signals with the help of JSI.
On the other hand traditional Frequency-hopping (FH) techniques are widely used in the military communication systems to achieve reliable information transmission. In the FH system, the information sequences are transmitted over time variable carrier frequency. If the FH technique and the iterative detection method are both effectively implied in the system, the performance - including jamming suppression performance, the reliability of the system, the spectrum efficiency - can be greatly improved. Therefore the iterative detection method and the iterative estimation method to suppress jamming in FH systems are studied in this paper.
In chapter two, the iterative detection principles and applications are introduced. The FH-CPM system model with serially connected channel coder is adopted. It's well known that continuous phase modulation (CPM) signals take on some attractive merits: high spectrum efficiency, fixed complex envelop, and it can be modulated by non-linear amplifier to avoid the cost of linear amplifier.
In Chapter three, the jamming suppression method of coherent FH-CPM is studied. By introducing an exact construction of digital phase modulations by superposition of amplitude modulated pulses (Laurent decomposition of CPM), the SISO algorithm is improved, and the complexity increasing caused by the response length of CPM is greatly reduced. Due to the interleaver between the modulator and the coder, the probability density function of the extrinsic information is difficult to be calculated. Here, extrinsic information transmission chart (EXIT) is employed to analyze the convergence character of the iteration. The simulation results demonstrate the system takes on good bit error rate (BER) performance in partial-band jamming (BPJ) and multi-tone jamming (MTJ) environment as well as in AWGN channel.
Chapter four is mainly about the SISO algorithm when non-coherent detection of CPM signals is applied. In this chapter, we propose an iterative tree search (ITS) algorithm based on Laurent decomposition, which can reduce the complexity of the demodulator while non-coherent detection is achieved. The convergence character analysis is also accomplished using EXIT. From the simulation results, we can see that the loss of BER performance is within 1.5dB compared to that of the system with coherent detector in AWGN channel.
In Chapter five, the partial-band jamming information (PBJSI) method is studied and the multi-tone jamming information (MTJSI) estimation method is proposed. The iterative estimation method of partial-band jamming is firstly studied, which brings nearly 3dB gain at aimed BER10~(-4). Secondly a multi-tone jamming estimation method is proposed in this paper. In this method the JSI and the threshold of deciding are iteratively updated, hence the problem of determining the threshold in frequency-domain estimation method is avoided. Meanwhile, the parameter of MTJ is estimated so that the jamming can be reconstructed and removed from the received signals. The simulation results prove that by introducing this method the receiver is almost free from MTJ.
另一方面,传统的跳频(Frequency Hopping,FH)技术具有较强的抗多径能力、抗人为干扰能力,如果把跳频通信系统与迭代检测技术结合在一起,则系统的综合性能指标,包括通信可靠性,保密性能,频谱利用率都会得到很大提升。因此,本文把跳频系统和连续相位调制(Continuous Phase Modulation,CPM)结合在一起,并研究了相应的迭代干扰抑制算法。
第二章简要介绍了迭代检测的原理与应用,并且建立了FH-CPM系统模型。CPM信号是一种有记忆非线性调制方式,通过CPM信号和信道码的串联形成具有类似串行级联卷积的信号结构,并在接收端进行联合解调译码迭代检测。CPM信号还有其他一些特点:它的信号能量集中,占用带宽小,对邻道的干扰小;是一种非线性调制,具有恒包络,可以使用效率更高的非线性放大器,而且其恒模特性还方便接收机进行信道估计。
第三章研究了相干FH-CPM迭代干扰抑制算法及其性能。并针对部分响应CPM信号解调复杂度高的问题,通过引入CPM信号的罗伦特分解,改进了软输入软数出解调算法,降低了接收机复杂度。在系统性能分析方面,由于迭代系统中交织器的引入,软输入软输出模块外信息的概率密度函数非常复杂,难以从数学上进行完备和准确的推导,因此采用了外信息转移图(Extrinsic InformationTransmission Chart,EXIT)进行了迭代收敛性的分析。仿真结果显示,这种系统方案和迭代检测算法在加性高斯白噪声(Additive White Gaussian Noise,AWGN)信道下有很好的误码率性能,在部分带干扰和多音干扰环境下也有较好的干扰抑制作用。
第四章研究了非相干FH-CPM迭代干扰抑制算法及其性能。提出了一种基于CPM信号罗伦特分解的迭代树搜索软输入软输出解调算法,并利用EXIT图分析了接收机的收敛特性。仿真结果显示,在迭代检测接收机中,跳内符号数为20时,采用非相干解调与相干解调的系统在加性高斯信道下所对应的误码率性能差距在1.5dB左右。
第五章研究了部分带干扰JSI估计算法,提出了一种多音干扰的JSI迭代估计算法。为了进一步提高系统的干扰抑制能力,文章考虑对接收信号进行迭代估计并把干扰状态信息输送给迭代检测器。针对部分带干扰,文章从干扰状态信息的后验概率出发,阐述了部分带干扰状态信息的迭代估计算法,并与迭代检测系统一起进行部分带干扰的抑制。仿真结果表明,迭代干扰估计器的引入,使得相干迭代干扰抑制在目标误码率10~(-4)处产生了接近3dB的性能增益:使得非相干迭代干扰抑制在目标误码率10~(-4)处产生了1dB的性能增益。针对多音干扰,本文提出了一种时域迭代估计算法,该算法能够通过迭代对干扰状态信息和干扰判决门限进行更新,避免了采用频域估计时干扰判决门限依靠经验值进行设定的缺点。仿真结果表明在原有迭代检测器的基础上,迭代干扰估计器的引入能够基本使得多音干扰信号被重建进而抵消,大大地改善了接收机的抗干扰性能。
In the severe interference environment of electronic warfare, it is important to suppress interference for reliability of systems. Iterative detection is an effective and promising signal processing method. The a prior information and the extrinsic information can be exchanged between soft-in soft -out (SISO) blocks, so that the optimal detection can be approached by introducing iterative detection. Moreover, jamming state information (JSI) can be calculated by iterative estimation. Combining the estimator and detector together, the receiver can greatly suppress the jamming signals with the help of JSI.
On the other hand traditional Frequency-hopping (FH) techniques are widely used in the military communication systems to achieve reliable information transmission. In the FH system, the information sequences are transmitted over time variable carrier frequency. If the FH technique and the iterative detection method are both effectively implied in the system, the performance - including jamming suppression performance, the reliability of the system, the spectrum efficiency - can be greatly improved. Therefore the iterative detection method and the iterative estimation method to suppress jamming in FH systems are studied in this paper.
In chapter two, the iterative detection principles and applications are introduced. The FH-CPM system model with serially connected channel coder is adopted. It's well known that continuous phase modulation (CPM) signals take on some attractive merits: high spectrum efficiency, fixed complex envelop, and it can be modulated by non-linear amplifier to avoid the cost of linear amplifier.
In Chapter three, the jamming suppression method of coherent FH-CPM is studied. By introducing an exact construction of digital phase modulations by superposition of amplitude modulated pulses (Laurent decomposition of CPM), the SISO algorithm is improved, and the complexity increasing caused by the response length of CPM is greatly reduced. Due to the interleaver between the modulator and the coder, the probability density function of the extrinsic information is difficult to be calculated. Here, extrinsic information transmission chart (EXIT) is employed to analyze the convergence character of the iteration. The simulation results demonstrate the system takes on good bit error rate (BER) performance in partial-band jamming (BPJ) and multi-tone jamming (MTJ) environment as well as in AWGN channel.
Chapter four is mainly about the SISO algorithm when non-coherent detection of CPM signals is applied. In this chapter, we propose an iterative tree search (ITS) algorithm based on Laurent decomposition, which can reduce the complexity of the demodulator while non-coherent detection is achieved. The convergence character analysis is also accomplished using EXIT. From the simulation results, we can see that the loss of BER performance is within 1.5dB compared to that of the system with coherent detector in AWGN channel.
In Chapter five, the partial-band jamming information (PBJSI) method is studied and the multi-tone jamming information (MTJSI) estimation method is proposed. The iterative estimation method of partial-band jamming is firstly studied, which brings nearly 3dB gain at aimed BER10~(-4). Secondly a multi-tone jamming estimation method is proposed in this paper. In this method the JSI and the threshold of deciding are iteratively updated, hence the problem of determining the threshold in frequency-domain estimation method is avoided. Meanwhile, the parameter of MTJ is estimated so that the jamming can be reconstructed and removed from the received signals. The simulation results prove that by introducing this method the receiver is almost free from MTJ.
引文
[1]查光明.扩频通信.陕西:西安电子科技大学出版社,2001,32-40
[2]Poor H V,Xiaodong Wang.Code-aided interference suppression for DS/CDMA communications.Interference suppression capability.IEEE Trans.Commun,2003,Vol.45:1101-1111
[3]C.Berrou,A.Glavieux,P.Thitimajshima.Near Shannon limit error-correcting coding and decoding,Proc.Int.Conf.Communications.1993,1064-1070.
[4]S.Benedetto,D.Divsalar,G.Montorsi.Serial concatenation of interleaved codes:Performance analysis,design,and iterative decoding,Telecommunications and Data Acquisition Progr.Rep,1996,Vol.42:126
[5]R.G.Gallager.Low-density parity-check codes.IRE Trans.Inform.Theory,1962,Vol.8:21-28.
[6]J.Hagenauer.The Turbo principle:Tutorial introduction and state of the art,in Proc.Int.Symp.Turbo Codes,Brest,France,1997,1-11.
[7]Berrou C,Glavieux A.Near optimum error-correcting coding and decoding:Turbo codes.IEEE Trans,Commun,1996,Vol.44:1261-1271
[8]W.Oh,K.Chen.Adaptive channel SNR estimation algorithm for turbo decoder.IEEE Commun.Lett.,Vol.14:255-257
[9]M.C.Valenti.Iterative channel estimation and decoding of pilot symbol assisted turbo codes over flat-fading channels.IEEE.Selected Areas in Communications,2001,Vol.19:1697-1705
[10]Komninakis C,Wesel R.D.Joint iterative channel estimation and decoding in flat correlated Rayleigh fading.IEEE J.Select Areas Communication,2001,Vol.19(9):1706-1717
[11]Wayne G.Iterative demodulation and decoding of frequency-hopped PSK in partial-band jamming.IEEE Journal on Selected areas in communications,2005,Vol.23(5):1026-1033
[12]Jang-Wook Moon.John M.Shea.,Tan F.Wong.Collaborative jamming mitigation on block-fading channels.IEEE,Transactions on Communications,Vol.54(6):343-487
[13]C.Brown.P.J.Vigneron.A Reduced complexity iterative non-coherent CPM detector for frequency hopped wireless military communication systems.IEEE,2005,Vol.5:17-20
[14] Zeinab Taghavi, Masoumeh Nasiri-Kenari. Iterative Multiuser Receiver for Coded MC-FH Multiple Access Systems in the Presence of Partial-Band Interference. Vehicular Technology Conference 2004, Vol. 23(3): 1899-1903
[15] Hesham El Gamal, and Evaggelos Geraniotis, Iterative Channel Estimation and Decoding for Convolutionally Coded Anti-Jam FH Signals, IEEE Transactions on Communications, 2002, Vol.50(2):1396-1423
[16] Pierre A. Laurent. Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses. IEEE Transactions on Communications, 1986, Vol. 34(2): 213-232
[17] De Jong, Y.L.C, Willink.T.J. Iterative tree search detection for MIMO wireless systems , IEEE Transactions on Communications, 2005, Vol.53(6):864-871
[18] Geng Wang, Qiang Li, Shaoqian Li, Partial-band jamming suppression with a noncoherent CPM detector, IEEE Communications and Mobile Conference, 2007 vol.29:1-5
[19] Benedetto S., Divsalar D., Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding. IEEE Transactions on Information Theory, 1998, Vol.44:223-236
[20] Wiberg, N. Simultaneous decoding and phase synchronization using iterative "turbo" decoding, IEEE, Information Theory. 1997. Proceedings. 1997 IEEE International Symposium on 1997 , Vol.52:117-132
[21] Wiberg, N.; Loeliger, H.-A.; Kotter, R. Codes and iterative decoding on general graphs, IEEE, Information Theory, 1995. Proceedings, 1995 IEEE International Symposium on 1995, Vol.32:17-22.
[22] Stephan ten Brink. Convergence Behavior of Iteratively Decoded Parallel Concatenated Codes. IEEE Transactions on Communications, 2001,Vol.49(10): 1061-1077
[23] Alexei Ashikhmin, Gerhard Kramer, and Stephan ten Brink. Extrinsic Information Transfer Functions: Model and Erasure Channel Properties. IEEE Transactions on Inforamation Theroty,2004, Vol. 50(11):573-590
[24] Eran Sharon, Alexei Ashikhmin, and Simon Litsyn. EXIT Functions for Binary Input Memoryless Symmetric Channels. IEEE Transactions on Communications, 2006, Vol.54(7):1111-1119
[25] D. J, C. MacKay. Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory, 1999, Vol.45(2): 399-431
[26]Tor Aulin,Carl-Erik.Continuous Phase Modulation-Part I:Full Response Signaling.IEEE Transactions on communications,1981,Vol.29(3):63-80
[27]Tor Aulin,Carl-Erik.Continuous Phase Modulation-Part Ⅱ:Partial Response Signaling.IEEE Transactions on communications,1981,Vol.29(3):490-512
[28]Balasubramanian,Michael P.Fitz,James V.Krogmeier.Optimal and Suboptimal ymbol-by-Symbol Demodulation of Continuous Phase Modulated Signals.IEEE Transactions on Communications,1998,Vol.46(12):147-160
[29]G Battail.Weighting the symbols decoded by the Viterbi algorithm.IEEE Annales Des Telecommunications,1987,Vol.19(3):32-43
[30]Giulio Colavolpe,Riccardo Raheli.Reduced-Complexity Detection and Phase Synchronization of CPM Signals.IEEE Transactions on Communications,1997,Vol.45(9):945-969
[31]Giulio Colavolpe,Alan Barbieri.On MAP Symbol Detection for ISI Channels Using the Ungerboeck Observation Model.IEEE Communications Letters,2005,Vol.9(8):71-73
[32]Frank R.Kschischang,Brendan J.Frey,Hans-Andrea Loeliger.Factor Graphs and the Sum-Product Algorithm.IEEE Transactions on Communications,2001,Vol.47(2):352-369
[33]S.Torgny,Andersson N.,Arne B.Sevensson.Continuous Phase Modulation Noncoherent Detection of Convolutionally Encoded Continuous Phase Modulation.IEEE Journal on Selected Areas in Communications,1989,Vol.7(9):86-102
[34]Marvin K.Simon,Dariush Divsalar.Maximum-Likelihood Block Detection of Noncoherent Continuous Phase Modulation.IEEE Transactions on Communications,1993,Vol.41(1):128-144
[35]Ketchum J W,Proakis J G Adaptive Algorithms for Estimating and Suppressing Narrow-Band Interference in PN Spread-Spectrum Systems.IEEE Transactions on Communication,1982,Vol.30:683-706
[36]Iltis R A,Milstein L B.Performance Analysis of Narrow-Band Interference Rejection Techniques in DS Spread-Spectrum Systems.IEEE Transactions on Communications,1984,Vol.32:1169-1177
[37]Young J A,Lehnert J S.Analysis of DFT-based frequency excision algorithms for direct-sequence spread-spectrum communications.IEEE Transactions on Communication,1998,Vol.46:63-74
[38]Thomas J,Geraniotis E.Narrowband.jammer suppression in coded DS-CDMA channels.IEEE Military Communication Conference,1999,Vol.31(2):831-835
[39] Zhi Chen, Shaoqian Li, Binhong Dong. Partial Band Jamming Rejection of Differential Frequency Hopping System with Product-Combining Receiver Over Rayleigh-fading Channel.IEEE, 2006 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings, Vol.22(5): 58-71
[40] Shad Laufer and Arie Reichman. Analysis of frequency-hopping systems in partial band jamming. IEEE, 1998, Vol.3(6): 522-543
[41] Fei Shang, Ben-qing Gao, Ge Liu, Xuan Xiao. Bit Error Performance Analysis of FH IMSK System in Different Multi-tone Noise Jamming. 2005 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings, 2005,Vol.4(5): 326-334.
[42] Ramon Agusti. Multiple Tone Interferers in an FH-MFSK Spread Spectrum Communication System. IEEE Transactions on Vehicular Technology, 1985, Vol.34(3): 91-99
[43] Malcolm D M.Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones.IEEE Trans.Signal Processing,1998,Vol.46(1): 141-148
[2]Poor H V,Xiaodong Wang.Code-aided interference suppression for DS/CDMA communications.Interference suppression capability.IEEE Trans.Commun,2003,Vol.45:1101-1111
[3]C.Berrou,A.Glavieux,P.Thitimajshima.Near Shannon limit error-correcting coding and decoding,Proc.Int.Conf.Communications.1993,1064-1070.
[4]S.Benedetto,D.Divsalar,G.Montorsi.Serial concatenation of interleaved codes:Performance analysis,design,and iterative decoding,Telecommunications and Data Acquisition Progr.Rep,1996,Vol.42:126
[5]R.G.Gallager.Low-density parity-check codes.IRE Trans.Inform.Theory,1962,Vol.8:21-28.
[6]J.Hagenauer.The Turbo principle:Tutorial introduction and state of the art,in Proc.Int.Symp.Turbo Codes,Brest,France,1997,1-11.
[7]Berrou C,Glavieux A.Near optimum error-correcting coding and decoding:Turbo codes.IEEE Trans,Commun,1996,Vol.44:1261-1271
[8]W.Oh,K.Chen.Adaptive channel SNR estimation algorithm for turbo decoder.IEEE Commun.Lett.,Vol.14:255-257
[9]M.C.Valenti.Iterative channel estimation and decoding of pilot symbol assisted turbo codes over flat-fading channels.IEEE.Selected Areas in Communications,2001,Vol.19:1697-1705
[10]Komninakis C,Wesel R.D.Joint iterative channel estimation and decoding in flat correlated Rayleigh fading.IEEE J.Select Areas Communication,2001,Vol.19(9):1706-1717
[11]Wayne G.Iterative demodulation and decoding of frequency-hopped PSK in partial-band jamming.IEEE Journal on Selected areas in communications,2005,Vol.23(5):1026-1033
[12]Jang-Wook Moon.John M.Shea.,Tan F.Wong.Collaborative jamming mitigation on block-fading channels.IEEE,Transactions on Communications,Vol.54(6):343-487
[13]C.Brown.P.J.Vigneron.A Reduced complexity iterative non-coherent CPM detector for frequency hopped wireless military communication systems.IEEE,2005,Vol.5:17-20
[14] Zeinab Taghavi, Masoumeh Nasiri-Kenari. Iterative Multiuser Receiver for Coded MC-FH Multiple Access Systems in the Presence of Partial-Band Interference. Vehicular Technology Conference 2004, Vol. 23(3): 1899-1903
[15] Hesham El Gamal, and Evaggelos Geraniotis, Iterative Channel Estimation and Decoding for Convolutionally Coded Anti-Jam FH Signals, IEEE Transactions on Communications, 2002, Vol.50(2):1396-1423
[16] Pierre A. Laurent. Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses. IEEE Transactions on Communications, 1986, Vol. 34(2): 213-232
[17] De Jong, Y.L.C, Willink.T.J. Iterative tree search detection for MIMO wireless systems , IEEE Transactions on Communications, 2005, Vol.53(6):864-871
[18] Geng Wang, Qiang Li, Shaoqian Li, Partial-band jamming suppression with a noncoherent CPM detector, IEEE Communications and Mobile Conference, 2007 vol.29:1-5
[19] Benedetto S., Divsalar D., Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding. IEEE Transactions on Information Theory, 1998, Vol.44:223-236
[20] Wiberg, N. Simultaneous decoding and phase synchronization using iterative "turbo" decoding, IEEE, Information Theory. 1997. Proceedings. 1997 IEEE International Symposium on 1997 , Vol.52:117-132
[21] Wiberg, N.; Loeliger, H.-A.; Kotter, R. Codes and iterative decoding on general graphs, IEEE, Information Theory, 1995. Proceedings, 1995 IEEE International Symposium on 1995, Vol.32:17-22.
[22] Stephan ten Brink. Convergence Behavior of Iteratively Decoded Parallel Concatenated Codes. IEEE Transactions on Communications, 2001,Vol.49(10): 1061-1077
[23] Alexei Ashikhmin, Gerhard Kramer, and Stephan ten Brink. Extrinsic Information Transfer Functions: Model and Erasure Channel Properties. IEEE Transactions on Inforamation Theroty,2004, Vol. 50(11):573-590
[24] Eran Sharon, Alexei Ashikhmin, and Simon Litsyn. EXIT Functions for Binary Input Memoryless Symmetric Channels. IEEE Transactions on Communications, 2006, Vol.54(7):1111-1119
[25] D. J, C. MacKay. Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory, 1999, Vol.45(2): 399-431
[26]Tor Aulin,Carl-Erik.Continuous Phase Modulation-Part I:Full Response Signaling.IEEE Transactions on communications,1981,Vol.29(3):63-80
[27]Tor Aulin,Carl-Erik.Continuous Phase Modulation-Part Ⅱ:Partial Response Signaling.IEEE Transactions on communications,1981,Vol.29(3):490-512
[28]Balasubramanian,Michael P.Fitz,James V.Krogmeier.Optimal and Suboptimal ymbol-by-Symbol Demodulation of Continuous Phase Modulated Signals.IEEE Transactions on Communications,1998,Vol.46(12):147-160
[29]G Battail.Weighting the symbols decoded by the Viterbi algorithm.IEEE Annales Des Telecommunications,1987,Vol.19(3):32-43
[30]Giulio Colavolpe,Riccardo Raheli.Reduced-Complexity Detection and Phase Synchronization of CPM Signals.IEEE Transactions on Communications,1997,Vol.45(9):945-969
[31]Giulio Colavolpe,Alan Barbieri.On MAP Symbol Detection for ISI Channels Using the Ungerboeck Observation Model.IEEE Communications Letters,2005,Vol.9(8):71-73
[32]Frank R.Kschischang,Brendan J.Frey,Hans-Andrea Loeliger.Factor Graphs and the Sum-Product Algorithm.IEEE Transactions on Communications,2001,Vol.47(2):352-369
[33]S.Torgny,Andersson N.,Arne B.Sevensson.Continuous Phase Modulation Noncoherent Detection of Convolutionally Encoded Continuous Phase Modulation.IEEE Journal on Selected Areas in Communications,1989,Vol.7(9):86-102
[34]Marvin K.Simon,Dariush Divsalar.Maximum-Likelihood Block Detection of Noncoherent Continuous Phase Modulation.IEEE Transactions on Communications,1993,Vol.41(1):128-144
[35]Ketchum J W,Proakis J G Adaptive Algorithms for Estimating and Suppressing Narrow-Band Interference in PN Spread-Spectrum Systems.IEEE Transactions on Communication,1982,Vol.30:683-706
[36]Iltis R A,Milstein L B.Performance Analysis of Narrow-Band Interference Rejection Techniques in DS Spread-Spectrum Systems.IEEE Transactions on Communications,1984,Vol.32:1169-1177
[37]Young J A,Lehnert J S.Analysis of DFT-based frequency excision algorithms for direct-sequence spread-spectrum communications.IEEE Transactions on Communication,1998,Vol.46:63-74
[38]Thomas J,Geraniotis E.Narrowband.jammer suppression in coded DS-CDMA channels.IEEE Military Communication Conference,1999,Vol.31(2):831-835
[39] Zhi Chen, Shaoqian Li, Binhong Dong. Partial Band Jamming Rejection of Differential Frequency Hopping System with Product-Combining Receiver Over Rayleigh-fading Channel.IEEE, 2006 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings, Vol.22(5): 58-71
[40] Shad Laufer and Arie Reichman. Analysis of frequency-hopping systems in partial band jamming. IEEE, 1998, Vol.3(6): 522-543
[41] Fei Shang, Ben-qing Gao, Ge Liu, Xuan Xiao. Bit Error Performance Analysis of FH IMSK System in Different Multi-tone Noise Jamming. 2005 IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings, 2005,Vol.4(5): 326-334.
[42] Ramon Agusti. Multiple Tone Interferers in an FH-MFSK Spread Spectrum Communication System. IEEE Transactions on Vehicular Technology, 1985, Vol.34(3): 91-99
[43] Malcolm D M.Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones.IEEE Trans.Signal Processing,1998,Vol.46(1): 141-148