基于频谱累积量的线性分组码检测识别方法

针对非合作信号处理中的线性分组码盲识别问题，提出了一种基于有限域傅里叶变换（Galois field Fourier transform， GFFT）的检测识别方法。该方法对接收码序列按不同长度进行分段，对分段码字进行有限域上的傅里叶变换并计算其频谱的累积量。通过频谱累积量的不同分布情况，可以估计出正确的分组码长度。同时从频谱累积量中找出码字生成多项式的根，进而得到码字的生成多项式。仿真实验验证了算法的有效性，并对算法的误码适应能力和计算复杂度进行了仿真分析，最后给出了在不同误码环境下最优的频谱累积次数。

Blind recognition of linear block code based on spectral cumulants

The problem that is described here is recovering a linear block code in non cooperative signal processing. An algorithm based on the Galois field Fourier transform (GFFT) is proposed. Firstly, the received bits are divided into code words with different lengths. Then the GFFT is operated on each code, the spectral cumulants are computed. The correct code length and roots of the generator polynomial can be estimated from the distributions of the spectral cumulants. The polynomial can be recovered according to the roots. The validity of the algorithm is verified by the simulation results. Case studies are presented to illustrate the performances of the proposed blind reconstruction method.