Shimon Peleg

The discrete polynomial-phase transform

The discrete polynomial-phase transform (DPT) is a new tool for analyzing constant-amplitude polynomial-phase signals. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly-varying amplitude, additive noise and nonpolynomial phase. The authors define the DPT, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms. A statistical accuracy analysis of the estimated parameters is also presented. >

Estimation and classification of polynomial-phase signals

The measurement of the parameters of complex signals with constant amplitude and polynomial phase, measured in additive noise, is considered. A novel new integral transform that is adapted for signals of this type is introduced. This transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance. The algorithms are extended to constant amplitude and continuous nonpolynomial phase signals. >

The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase

The authors derive the Cramer-Rao lower bound (CRLB) for complex signals with constant amplitude and polynomial phase, measured in additive Gaussian white noise. The exact bound requires numerical inversion of an ill-conditioned matrix, while its O(N/sup -1/) approximation is free of matrix inversion. The approximation is tested for several typical parameter values and is found to be excellent in most cases. The formulas derived are of practical value in several radar applications, such as electronic intelligence systems (ELINT) for special pulse-compression radars, and motion estimation from Doppler measurements. Consequently, it is of interest to analyze the best possible performance of potential estimators of the phase coefficients, as a function of signal parameters, the signal-to-noise ratio, the sampling rate, and the number of measurements. This analysis is carried out. >

Linear FM signal parameter estimation from discrete-time observations

The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations. An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed. The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima. The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above. The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar. A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations. >

Multicomponent signal analysis using the polynomial-phase transform

We consider the problem of estimating signals consisting of multiple components of the form b(n)exp{J/spl phi/(n)} where b(n) is a constant or a slowly varying amplitude, and the /spl phi/(n) is a polynomial function of time. We present an estimation algorithm based on the discrete polynomial transform and illustrate its performance by several examples. The proposed algorithm is computationally much simpler than the maximum likelihood estimator for this problem.

The achievable accuracy in estimating the instantaneous phase and frequency of a constant amplitude signal

The approach is based on modeling the signal phase by a polynomial function of time on a finite interval. The phase polynomial is expressed as a linear combination of the Legendre basis polynomials. First, the Cramer-Rao bound (CRB) of the instantaneous phase and frequency of constant-amplitude polynomial-phase signals is derived. Then some properties of the CRBs are used to estimate the order of magnitude of the bounds. The analysis is extended to signals whose phase and frequency are continuous but not polynomial. The CRB can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood. The maximum-likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the CRB of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations. >

A technique for estimating the parameters of multiple polynomial phase signals

An iterative algorithm for estimating the parameters of multiple superimposed polynomial phase signals is presented. The algorithm is based on the ability of the discrete polynomial transform (DPT) to estimate the parameters of a polynomial phase signal in the presence of other interfering signals. The parameters of one of the signals having been estimated, it can be filtered out from the composite signal. The procedure is then applied to the remainder, which contains a smaller number of components. In extensive testing it was found that the algorithm works very well in general. It is able to reliably separate multiple signals and to accurately estimate their parameters.<<ETX>>

The discrete polynomial transform (DPT), its properties and applications

The discrete polynomial transform (DPT) is a new tool for analyzing constant-amplitude continuous-phase signals. It is based on modeling the signal phase by a polynomial function of time. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly varying amplitude, additive noise, and nonpolynomial phase. Its effect on polynomial-phase signals is shown. Its main mathematical properties are listed and proofs are provided for some. It is shown how to use those properties to derive estimation and classification algorithms for continuous-phase signals. Some recent results on the statistical accuracy of these algorithms are stated. Applications of the DPT to certain radar and communication problems are discussed.<<ETX>>

Multi-component signal analysis using the polynomial transform

An iterative algorithm for estimating the parameters of multiple superimposed polynomial phase signals is presented. The algorithm is based on the ability of the discrete polynomial transform (DPT) to estimate the parameters of a polynomial phase signal in the presence of other interfering signals. Once the parameters of one of the signals are estimated, it can be filtered out from the composite signal. The procedure is then applied to the remainder, which contains a small number of components. The DPT is applied to the analysis of the signal emitted by the big brown bat.<<ETX>>

Signal estimation using the discrete polynominal transform

The authors develop an iterative procedure for estimating the parameters of a signal consisting of multiple polynomial-phase components with time-varying amplitudes. The proposed algorithm is based on the discrete polynomial transform (DPT), and shares its computational simplicity. Preliminary experimentation with the algorithm has shown that it is able to provide accurate parameter estimates. A numerical example is included.<<ETX>>