Results of applying the algorithms based on the theory of optimal detection and optimal estimation to analysis of the envelope soliton

The problems on the optimal detection and optimal estimation of envelope soliton parameters have been solved jointly via the quadrature reception method. The expressions for detection characteristics, signal parameter estimates, and relative errors have been derived. It is demonstrated that the false alarm and missing probabilities are usually several percents and the relative errors do not exceed 5–30%. It has been found that the estimated parameters agree well with the real ones if the signal-to-noise ratio is close to unity. The proposed algorithms are shown to have an advantage over the classical and modern spectrum estimation methods when they are employed to reveal the envelope soliton against the background of Gaussian quasiwhite noise.