Unbiased Self-synchronous Scrambler Identification Based on Log Conditional Likelihood Ratio
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摘要: 为克服现有无偏自同步扰码识别算法在低信噪比(SNR)下存在适应性差的缺点，该文提出一种基于对数条件似然比的软判决识别方法。该方法首先构建了线性分组码自同步加扰和卷积码自同步加扰的对偶向量积线性约束方程；然后推导了基于软判决的对数条件似然比函数衡量方程的成立概率，并分析了其均值和方差的分布特性；最后通过2元假设和推导的相应判别门限来完成两种自同步加扰的识别。仿真结果表明，所提算法能够在低信噪比下完成生成多项式的识别，具有较好的适应能力，与基于求解代价函数的识别方法相比，在信噪比低于3 dB时的算法识别率得到较大提高，识别率为90%时，约有3 dB的性能增益。Abstract: To overcome the drawback of poor adaptability of existing unbiased self-synchronous scrambling code recognition algorithms at low Signal-to-Noise Ratios (SNR), a soft-judgement recognition method based on the log conditional likelihood ratio is proposed. Firstly, the linear constraint equations for the pairwise even-vector product of the self-synchronous scrambler of linear grouping codes and the self-synchronous scrambler of convolutional codes are constructed, and then the log likelihood ratio function is introduced, the log conditional likelihood ratio function based on the soft judgment is constructed, and the distribution characteristics of its mean and variance are analyzed. Finally the identification of self-synchronous scrambler of linear grouping codes and self-synchronous scrambler of convolutional codes is accomplished through binary assumption and the derived coresponding judgement threshold value. The simulations show that the proposed algorithm is able to complete the recognition of generating polynomials at low signal-to-noise ratios, and has a good low signal-to-noise adaptation capability. Compared with the recognition method based on solving the cost function, the recognition rate of the algorithm is greatly improved at signal-to-noise ratios below 3 dB, and when the recognition rate is 90%, the proposed algorithm achieves a performance gain of about 3 dB.
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表 1 卷积码参数设定(不同码重)
码重$w$ 生成多项式 3 [$1,1 + {D^5}$] 5 [$1 + {D^5},1 + {D^4} + {D^5}$] 7 [$1 + {D^3} + {D^5},1 + {D^3} + {D^4} + {D^5}$] 9 [$1 + {D^2} + {D^4} + {D^5},1 + {D^2} + {D^3} + {D^4} + {D^5}$] 11 [$1 + D + {D^3} + {D^4} + {D^5},1 + D + {D^2} + {D^3} + {D^4} + {D^5}$] 
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表 2 卷积码参数设定(不同编码约束长度)
编码约束长度${\text{sL}}$ 生成多项式 8 [$1 + {D^3},1 + {D^2} + {D^3}$] 10 [$1 + {D^4},1 + {D^3} + {D^4}$] 12 [$1 + {D^5},1 + {D^4} + {D^5}$] 14 [$1 + D,1 + D + {D^6}$]
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