Blind reconstruction of linear scrambler

An algorithm based on eigenanalysis technique and Walsh-Hadamard transform (WHT) is proposed. The algorithm contains two steps. Firstly, the received sequence is divided into temporal windows, and a covariance matrix is computed. The linear feedback shift register (LFSR) sequence is reconstructed from the first eigenvector of this matrix. Secondly, equations according to the recovered LFSR sequence are constructed, and the Walsh spectrum corresponding to the equations is computed. The feedback polynomial of LFSR is estimated from the Walsh spectrum. The validity of the algorithm is verified by the simulation result. Finally, case studies are presented to illustrate the performance of the blind reconstruction method.