Confidence evaluation for blind analysis of LFM/BPSK hybrid signals based on extreme value theory

The confidence evaluation of a blind analysis for a hybrid modulation scheme combining binary phase shift keying (BPSK) with linear frequency modulation (LFM) signals is derived herein to statistically decide whether an individual processing result is correct by using only the observed signal and analysis results, including modulation identification and corresponding parameter estimations. They formulate the problem using a binary hypothesis, where the null hypothesis states that modulation recognition is correct, and the errors of parameter estimates are all less than some particular metrics (i.e. the analysis result is confident). An auxiliary signal is constructed by using the identified modulation model and corresponding estimated parameters. The modified correlation spectrum between the observed and auxiliary signals is computed accordingly. The spectrum does not exhibit any peaks under the null hypothesis (H0) but does under the alternative hypothesis. This provides the basis of a useful discriminating feature for verifying the confidence of the analysis result. They prove that the extreme values of the modified correlation spectrum under H0 have a Gumbel distribution. A goodness-of-fit test based on the Kolmogorov–Smirnov is used to perform a confidence evaluation of the analysis result of the LFM/BPSK signal. The effectiveness of the algorithm is demonstrated in extensive joint simulation experiments.