Statistical Characteristics of the Energy-Concealed Phase-Manipulated Signal

Abstract

The law of distribution of the output effect differs from the normal one at the output of the receiving path realized on the basis of autocorrelation algorithm with quadrature processing. When there is no signal at the input of the receiver, the distribution of the output effect corresponds to Rayleigh’s or Rayleigh – Rice’s law in condition of its presence. The probability density distribution at the output of an incoherent auto correlation receiver with quadrature processing is considered in relation to the input level of the energy-concealed phase-manipulated signal. In order to detect a useful signal it is necessary that, at the output of the receiver, the signal / noise ratio exceeds the detection threshold determined by the Neumann – Pearson criterion according to the given probability of false alarm. The level of the signal-to-noise ratio at the output of an incoherent autocorrelation receiver with quadrature processing has been calculated. A characteristic feature of the presented graphs is the linear dependence of the output signal / noise ratio relative to the input signal. This feature is observed in the input signal / noise ratio which is less than one. The curves for the distribution of the probability density of the input signal mix and noise corresponding to the generalized Rayleigh’s law (Rayleigh-Rice) are constructed in the book. There is a shift of curves for the abscissa axis according to the given probabilities of false alarms and accumulation time (observation). It is evident from the given graphs that the offset of the abscissa of the input signal value / noise ratio significantly depends on the accumulation of the input mixture time. The curves for detecting an energy-concealed phase-manipulated signal by a non-coherent autocorrelation receiver with quadrature processing on the basis of the probability density distribution are obtained. The results of the calculations indicate that detection of a phase-manipulated signal on the background of "white" noise is possible in case of an input-to-noise ratio of less than one, that is, up to -32 dB in real time (up to 0.1 s).