Performance Statistics of Autoregressive Short and Ultrashort Signal Detectors

Abstract

Introduction. Parametric spectral estimation methods provide an improved level of frequency resolution compared to matched signal processing conventionally used in radar technology. This renders these methods promising for application in cases where the sample size of a spatial or temporal signal is strictly limited. At the same time, parametric methods are not optimal when receiving single signals against the background of normal uncolored additive noise. Therefore, parametric methods can be used as independent approaches provided that, first, working detection statistics are selected and justified and, second, that detection characteristics and noise immunity are constructed and analyzed.Aim. This paper investigates modified detection statistics of the parametric Burg method, characterized by the simplicity of decision functions and the capacity to provide a constant false alarm probability under varying additive noise levels.Materials and methods. Statistical computer simulation of the detection algorithms under consideration was conducted. This method is widely used in the analysis of parametric methods of signal processing. The detection characteristics obtained in the work were compared using the well-known Burg harmonic mean method, which involves the lowest computational costs.Results. The paper presents original decision functions derived from the transformation of power spectral density estimates of the Burg method. The detection characteristics and immunity to signal-like interference of the modified Burg method are obtained and investigated, providing the basis for a comparative analysis of the proposed partial detection statistics. These are shown to retain the property of invariance of false alarm probability to the level of normal white noise.Conclusion. The obtained detection and noise immunity characteristics for ultrashort and short signal samples allow us to recommend the parametric Burg harmonic mean method, implemented on the basis of a forward and backward linear prediction algorithm, as an independent signal processing method under strict restrictions imposed on the size of the analyzed sample of spatial-temporal signals.