| Citation: | TAN J Y，ZHANG L M，ZHONG Z G. Estimation of initial state of scrambler based on piecewise solution of error equation[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（11）：3039-3046 （in Chinese） doi: 10.13700/j.bh.1001-5965.2022.0046
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A method of initial state estimation of scrambling code based on solving the error equation is provided in order to address the issue of a low correct estimation rate of the initial state of scrambling code under a low signal-to-noise ratio. According to the initial state recurrence relation, the received soft decision sequence is used to establish the error-containing equation, and the initial state estimation problem is transformed into the solution of the error-containing equation system. The average check coincidence degree is proposed to measure the possibility of the establishment of the error-containing equation system, and the initial state estimation is completed by traversing the set of initial states. A piecewise solution equation method for finding the calibration equation is proposed, which greatly reduces the number of initial states that need to be traversed under high-order numbers. The experimental results show that the proposed algorithm can reach more than 90% of the correct estimation rate of the scrambled code initial state with a signal-to-noise ratio of 0 dB, which is about 1-2 dB performance improvement compared with the traditional fast correlation attack algorithm for convolutional codes.
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