Concerning the problem that the performance analysis method of Luby Transform (LT) codes under Gaussian elimination decoding algorithm is complicated and inaccurate, a novel performance analysis method based on probability transfer function was proposed. Firstly, for two LT codes with simple uniform degree distribution, the precise performance was studied and its quantitative expression was given. Secondly, the general LT code was investigated, and a simple but effective qualitative analysis method was proposed. Finally, the simulation work was done to verify the new method. In the comparison experiments with the traditional method which only gives the upper and the lower bounds of the rank of generated matrix, the maximum error of performance analysis results for simple uniform degree LT codes reduces to 0.0124, and the complexity of general LT codes decrease to O( k ²). Theoretical analysis shows that the proposed method can effectively guide the optimization design of LT codes in communication area.

Since most of the spoofing detection methods working in the satellite navigation receiver tracking phase can only detect one spoofing signal transmitted from single source, a novel spoofing detection method based on the statistical property analysis of carrier tracking loop was proposed. Firstly, the shortcomings of the existing spoofing detection methods were analyzed. Secondly, the received signal model under the spoofing attack environment was established and the statistical character of the complex signal which composites the real and spoofing signals was analyzed. Theoretical analysis shows that when the frequencies of the spoof signal and real signal are different, the novel algorithm can detect the spoofing signal since the I-branch signal's amplitude is not stable. The simulation results show that the proposed method can achieve 100% detection probability under 2% false alarm probability when the carrier-to-noise ratio of the received signal in the normal range (28 dB·Hz to 50 dB·Hz). By using the proposed algorithm, the spoofing signals transmitted from different sources can be detected, and the performance is greatly improved compared with the existing methods (about 1 dB under the same carrier-to-noise ratio, and about 4 dB under the same interference-to-signal ratio).