Yu. E. Korchagin

Reception of a Signal with Unknown Duration

The maximum likely and optimal (Bayesian) algorithms for detecting an arbitrary-shaped signal observed against the background of Gaussian white noise and for measuring the duration are synthesized. Exact expressions for the characteristics of the maximum likely algorithms are found. The characteristics of the Bayesian algorithms are obtained using computer simulations.

Efficiency of estimating duration of a signal with unknown amplitude

Quasi-likelihood and maximum likelihood algorithm for estimating duration of a signal with arbitrary share and unknown amplitude are synthesized. Operation efficiency characteristics for the synthesized algorithms are determined. Operation of the synthesized algorithms is verified and applicability limits for asymptotic expressions are obtained using computer emulation

Exact formulas for computation of reception characteristics of a signal with unknown appearance and disappearance times

We consider the performance of the maximum-likelihood algorithm for detection and measurement of appearance and disappearance times of an arbitrary waveform signal observed against additive white Gaussian noise. We find exact expressions for detection error probabilities and densities of estimated appearance and disappearance times.

Optimal Detection of a Signal with Unknown Appearance and Disappearance Times

We obtain maximum likelihood and optimal (Bayesian) algorithms for detection and measurement of moments of appearance and disappearance of a signal having arbitrary shape and observed in additive white Gaussian noise. Asymptotic expressions for characteristics of the maximum likelihood algorithms are obtained. By means of computer modeling, characteristics of the Bayesian algorithms are found.

Amplitude estimation of signal with unknown duration

Quasilikelihood and maximum likelihood algorithms for estimating the amplitude of arbitrary waveform signal with unknown duration have been synthesized. Characteristics of the synthesized algorithms have been also found.

Detection of radio signals that appear and disappear at unknown moments

The most plausible algorithm for the detection of a radio signal with unknown amplitude, phase and the moments of appearance and disappearance is synthesized. A two-channel quasi-optimal detector of radio signal the structure of which is simpler than the structure of the optimal detector is proposed. Asymptotic characteristics of the quasi-optimal detector are determined.

Estimation of the radio pulse duration with unknown phase

Quasi-likelihood and maximum likelihood algorithms for estimating the duration of a radio signal having arbitrary waveform and unknown phase were synthesized. Asymptotically exact characteristics of the estimates were also found.

Efficiency of the Detection of a Specific Wideband Signal under a Priori Parametric Uncertainty

A quasi-plausible algorithm is synthesized for detection of ultrawideband quasi-radio-signal with arbitrary shape and unknown amplitude, initial phase and duration. Statistical characteristics of the efficiency of the proposed algorithm (false-alarm and signal-omission probabilities) are determined. A decrease in the detection efficiency due to a priori ignorance of the signal parameters is characterized.

Estimation of the Initial Phase of Narrowband Radio Signal with Unknown Amplitude and Duration

The quasi-likelihood and maximum likelihood algorithms for estimating the initial phase of radio signal with arbitrary shaped envelope and unknown duration and amplitude have been synthesized. Schematic block diagrams of initial phase meters are proposed. Characteristics of the synthesized algorithms were determined, and errors of the initial phase estimates were compared. The structure of quasi-likelihood estimate of the initial phase is shown to be invariant with respect to the lack of knowledge of radio signal amplitude. However, a mismatch between the expected value of signal duration and its true value can lead to a marked increase of dispersion of the initial phase quasi-likelihood estimate. The loss in accuracy of the initial phase estimate due to a priori lack of knowledge of signal duration has been determined. Analytical expressions for statistical characteristics of maximum likelihood estimate of initial phase at large signal-to-noise ratios are shown to coincide asymptotically with the characteristics of maximum likelihood estimate of the initial phase of radio signal with a priori known amplitude and duration. Therefore, a priori unknown signal duration (asymptotically with an increase of signal-to-noise ratio) does not affect the accuracy of the maximum likelihood estimate of initial phase. The computer methods of statistical simulation were used to determine the applicability limits of asymptotic expressions for characteristics of the maximum likelihood estimate in respect of signals with linear and exponential envelopes.

Amplitude estimation of rectangular narrow-band radio pulse with unknown duration and initial phase

This study investigates algorithms for the estimation of amplitude of the radio signal with rectangular envelope and unknown duration and initial phase. The synthesis and analysis of quasi-likelihood and quasi-coherent estimation algorithm have been performed. This algorithm implies that the unknown duration and initial phase are replaced with certain expected values of these parameters. The loss in accuracy of amplitude estimation owing to the a priori lack of knowledge of the duration and the initial phase is analyzed. The quasi-likelihood noncoherent algorithm for amplitude estimation with the initial phase adaptation is synthesized and its statistical characteristics such as the estimate bias and variance are determined. The relationships of the loss in estimation accuracy owing to the a priori lack of knowledge of signal duration are derived. The maximum likelihood algorithm for amplitude estimation was synthesized and analyzed. This algorithm implies that the unknown duration and the initial phase are replaced with their maximum likelihood estimates. The gain in accuracy of the maximum likelihood estimate as compared to the quasi-likelihood ones was investigated. It is shown that a priori lack of knowledge of the signal duration does not affect asymptotically the accuracy of maximum likelihood estimate of amplitude at large values of signal-to-noise ratio.