Abstract
Self-synchronous scramblers are more difficult to blindly estimate than synchronous scramblers because their input sequence affects the state of the scrambler's linear feedback shift register. There has been much research on the estimation of synchronous scramblers and relatively little on the estimation of self-synchronous scramblers. For non-cooperative contexts, this paper proposes a method for the estimation of a self-synchronous scrambler in direct sequence spread spectrum systems. We blindly estimate the self-synchronous scrambling parameter, the feedback polynomial, using the repeated patterns by a spreading code, the linearity between the bits in a scrambling sequence, and the coidentity of the self-synchronous scrambled sequence and the linear feedback shift register states. To validate the proposed method, we show the estimation performance in terms of the computational complexity, required minimum scrambled sequence length, execution time, and detection probability.
Highlights
Direct Sequence Spread Spectrum (DSSS) is widely used for secure communications in both cooperative and non-cooperative contexts
For non-cooperative contexts, this paper proposed a method to estimate a self-synchronous scrambler without any bias condition and analyzed the estimation performance in direct sequence spread spectrum systems
A part of the scrambled sequence becomes the linear feedback shift register (LFSR) state in a self-synchronous scrambler: we were able to get linear equations for feedback polynomial coefficients by removing the scrambler input sequence composed of message and spreading code in the scrambled sequence
Summary
Direct Sequence Spread Spectrum (DSSS) is widely used for secure communications in both cooperative and non-cooperative contexts. In Algorithm 1, to estimate the feedback polynomial of n degree, it is required to input bits longer than or equal to (k + 1) n + 2-bit length sequence for constructing the simultaneous linear equation. If there are errors in the received scrambled sequence due to noise, it becomes highly probable that the solution of the simultaneous linear equation of Step 3 in Algorithm 1 will differ from the original feedback polynomial. We can see that when one of the linear equations in the simultaneous linear equation of Step 3 in Algorithm 1 is incorrect, the probability that the output polynomial will be the multiple of the original feedback polynomial for the LFSR, 1 − 2n−H−1, is higher than the probability that the output polynomial will be the random polynomial, 2−H−1, from Theorem 1 This is a clue for the estimation of the self-synchronous scrambler in DSSS systems. If it is not an irreducible polynomial, we calculate additional GCDs with the most commonly occurring polynomials until we find the irreducible polynomial GCD
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